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Anshumali Shrivastava

Anshumali Shrivastava appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Machine LearningInformation RetrievalData Structures and AlgorithmsArtificial IntelligenceDatabasesDistributed, Parallel, and Cluster ComputingMethodologyComputationInformation Theorymath.ITComputer VisionCryptography and SecurityApplicationsComputational Geometryeess.SPGenomicsLogic in Computer Sciencemath.OCNeural and Evolutionary ComputingRobotics

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Published work

44 published item(s)

preprint2026arXiv

70% Size, 100% Accuracy: Lossless LLM Compression for Efficient GPU Inference via Dynamic-Length Float (DFloat11)

Large-scale AI models, such as Large Language Models (LLMs) and Diffusion Models (DMs), have grown rapidly in size, creating significant challenges for efficient deployment on resource-constrained hardware. In this paper, we introduce Dynamic-Length Float (DFloat11), a lossless compression framework that reduces LLM and DM size by 30% while preserving outputs that are bit-for-bit identical to the original model. DFloat11 is motivated by the low entropy in the BFloat16 weight representation of LLMs, which reveals significant inefficiency in the existing storage format. By applying entropy coding, DFloat11 assigns dynamic-length encodings to weights based on frequency, achieving near information-optimal compression without any loss of precision. To facilitate efficient inference with dynamic-length encodings, we develop a custom GPU kernel for fast online decompression. Our design incorporates the following: (i) compact, hierarchical lookup tables (LUTs) that fit within GPU SRAM for efficient decoding, (ii) a two-phase GPU kernel for coordinating thread read/write positions using lightweight auxiliary variables, and (iii) transformer-block-level decompression to minimize latency. Experiments on Llama 3.3, Qwen 3, Mistral 3, FLUX.1, and others validate our hypothesis that DFloat11 achieves around 30% model size reduction while preserving bit-for-bit identical outputs. Compared to a potential alternative of offloading parts of an uncompressed model to the CPU to meet memory constraints, DFloat11 achieves 2.3--46.2x higher throughput in token generation. With a fixed GPU memory budget, DFloat11 enables 5.7--14.9x longer generation lengths than uncompressed models. Notably, our method enables lossless inference of Llama 3.1 405B, an 810GB model, on a single node equipped with 8x80GB GPUs.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

LeanQuant: Accurate and Scalable Large Language Model Quantization with Loss-error-aware Grid

Large language models (LLMs) have shown immense potential across various domains, but their high memory requirements and inference costs remain critical challenges for deployment. Post-training quantization (PTQ) has emerged as a promising technique to reduce memory requirements and decoding latency. However, recent accurate quantization methods often depend on specialized computations or custom data formats to achieve better model quality, which limits their compatibility with popular frameworks, as they require dedicated inference kernels tailored to specific hardware and software platforms, hindering wider adoption. Furthermore, many competitive methods have high resource requirements and computational overhead for quantizing models, making it challenging to scale them to hundreds of billions of parameters. In response to these challenges, we propose LeanQuant (Loss-Error-Aware Network Quantization), a novel quantization method that is accurate, versatile, and scalable. In the existing popular iterative loss-error-based quantization framework, we identify a critical limitation in prior methods: the min-max affine quantization grid fails to preserve model quality due to outliers in inverse Hessian diagonals. To overcome this fundamental issue, we propose learning loss-error-aware grids, instead of using non-adaptive min-max affine grids. Our approach not only produces quantized models that are more accurate but also generalizes to a wider range of quantization types, including affine and non-uniform quantization, enhancing compatibility with more frameworks. Extensive experiments with recent LLMs demonstrate that LeanQuant is highly accurate, comparing favorably against competitive baselines in model quality, and scalable, achieving very accurate quantization of Llama-3.1 405B, one of the largest open-source LLMs to date, using two Quadro RTX 8000-48GB GPUs in 21 hours.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Sketch to Adapt: Fine-Tunable Sketches for Efficient LLM Adaptation

Adapting pre-trained large language models (LLMs) is crucial but challenging due to their enormous size. Parameter-efficient fine-tuning (PEFT) techniques typically employ additive adapters applied to frozen model weights. To further reduce memory usage, model weights are often compressed through quantization. However, existing PEFT methods often yield suboptimal model quality because they rely on restrictive assumptions, such as low-rank constraints on adapters to limit the number of trainable parameters. We find that sketching, a popular data compression technique, can serve as an efficient LLM adaptation strategy while avoiding the low-rank assumption. We introduce SketchTune, a compressive adaptation strategy that compresses LLM weights into compact fine-tunable sketches, integrating compression and adaptation into a unified framework. This integration eliminates the need for complex two-path computation in existing PEFT techniques, enabling faster and more memory-efficient training and inference. SketchTune is supported by mathematical insights into matrix classes that are better approximated using sketching rather than low-rank methods. Our extensive evaluations with Llama and Mistral models demonstrate that SketchTune outperforms leading PEFT methods across diverse tasks while using substantially smaller base models and comparable trainable parameters. As a highlight, SketchTune outperforms LoRA, DoRA, and S2FT on commonsense and math benchmarks using 2.6-3.5$\times$ smaller base models and exceeds LoftQ in accuracy by 14.48% on GSM8K with 7.3$\times$ fewer trainable parameters. Our code is available at https://github.com/LeanModels/SketchTune.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Superintelligent Retrieval Agent: The Next Frontier of Information Retrieval

Retrieval-augmented agents are increasingly the interface to large organizational knowledge bases, yet most still treat retrieval as a black box: they issue exploratory queries, inspect returned snippets, and iteratively reformulate until useful evidence emerges. This approach resembles how a newcomer searches an unfamiliar database rather than how an expert navigates it with strong priors about terminology and likely evidence, and results in unnecessary retrieval rounds, increased latency, and poor recall. We introduce \textit{SuperIntelligent Retrieval Agent} (SIRA), which defines \emph{superintelligence} in retrieval as the ability to compress multi-round exploratory search into a single corpus-discriminative retrieval action. SIRA does not merely ask what terms are relevant to the query; it asks which terms are likely to separate the desired evidence from corpus-level confusers. On the corpus side, an LLM enriches each document offline with missing search vocabulary; on the query side, it predicts evidence vocabulary omitted by the query; and document-frequency statistics as a tool call to filter proposed terms that are absent, overly common, or unlikely to create retrieval margin. The final retrieval step is a single weighted BM25 call combining the original query with the validated expansion. Across ten BEIR benchmarks and downstream question-answering tasks, SIRA achieves the significantly superior performance outperforming dense retrievers and state-of-the-art multi-round agentic baselines, demonstrating that one well-formed lexical query, guided by LLM cognition and lightweight corpus statistics, can exceed substantially more expensive multi-round search while remaining interpretable, training-free, and efficient.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Distributed SLIDE: Enabling Training Large Neural Networks on Low Bandwidth and Simple CPU-Clusters via Model Parallelism and Sparsity

More than 70% of cloud computing is paid for but sits idle. A large fraction of these idle compute are cheap CPUs with few cores that are not utilized during the less busy hours. This paper aims to enable those CPU cycles to train heavyweight AI models. Our goal is against mainstream frameworks, which focus on leveraging expensive specialized ultra-high bandwidth interconnect to address the communication bottleneck in distributed neural network training. This paper presents a distributed model-parallel training framework that enables training large neural networks on small CPU clusters with low Internet bandwidth. We build upon the adaptive sparse training framework introduced by the SLIDE algorithm. By carefully deploying sparsity over distributed nodes, we demonstrate several orders of magnitude faster model parallel training than Horovod, the main engine behind most commercial software. We show that with reduced communication, due to sparsity, we can train close to a billion parameter model on simple 4-16 core CPU nodes connected by basic low bandwidth interconnect. Moreover, the training time is at par with some of the best hardware accelerators.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Efficient model compression with Random Operation Access Specific Tile (ROAST) hashing

Advancements in deep learning are often associated with increasing model sizes. The model size dramatically affects the deployment cost and latency of deep models. For instance, models like BERT cannot be deployed on edge devices and mobiles due to their sheer size. As a result, most advances in Deep Learning are yet to reach the edge. Model compression has sought much-deserved attention in literature across natural language processing, vision, and recommendation domains. This paper proposes a model-agnostic, cache-friendly model compression approach: Random Operation Access Specific Tile (ROAST) hashing. ROAST collapses the parameters by clubbing them through a lightweight mapping. Notably, while clubbing these parameters, ROAST utilizes cache hierarchies by aligning the memory access pattern with the parameter access pattern. ROAST is up to $\sim 25 \times$ faster to train and $\sim 50 \times$ faster to infer than the popular parameter sharing method HashedNet. Additionally, ROAST introduces global weight sharing, which is empirically and theoretically superior to local weight sharing in HashedNet, and can be of independent interest in itself. With ROAST, we present the first compressed BERT, which is $100\times - 1000\times$ smaller but does not result in quality degradation. These compression levels on universal architecture like transformers are promising for the future of SOTA model deployment on resource-constrained devices like mobile and edge devices

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Fast Processing and Querying of 170TB of Genomics Data via a Repeated And Merged BloOm Filter (RAMBO)

DNA sequencing, especially of microbial genomes and metagenomes, has been at the core of recent research advances in large-scale comparative genomics. The data deluge has resulted in exponential growth in genomic datasets over the past years and has shown no sign of slowing down. Several recent attempts have been made to tame the computational burden of sequence search on these terabyte and petabyte-scale datasets, including raw reads and assembled genomes. However, no known implementation provides both fast query and construction time, keeps the low false-positive requirement, and offers cheap storage of the data structure. We propose a data structure for search called RAMBO (Repeated And Merged BloOm Filter) which is significantly faster in query time than state-of-the-art genome indexing methods- COBS (Compact bit-sliced signature index), Sequence Bloom Trees, HowDeSBT, and SSBT. Furthermore, it supports insertion and query process parallelism, cheap updates for streaming inputs, has a zero false-negative rate, a low false-positive rate, and a small index size. RAMBO converts the search problem into set membership testing among $K$ documents. Interestingly, it is a count-min sketch type arrangement of a membership testing utility (Bloom Filter in our case). The simplicity of the algorithm and embarrassingly parallel architecture allows us to stream and index a 170TB whole-genome sequence dataset in a mere 9 hours on a cluster of 100 nodes while competing methods require weeks.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Learning to Retrieve Relevant Experiences for Motion Planning

Recent work has demonstrated that motion planners' performance can be significantly improved by retrieving past experiences from a database. Typically, the experience database is queried for past similar problems using a similarity function defined over the motion planning problems. However, to date, most works rely on simple hand-crafted similarity functions and fail to generalize outside their corresponding training dataset. To address this limitation, we propose (FIRE), a framework that extracts local representations of planning problems and learns a similarity function over them. To generate the training data we introduce a novel self-supervised method that identifies similar and dissimilar pairs of local primitives from past solution paths. With these pairs, a Siamese network is trained with the contrastive loss and the similarity function is realized in the network's latent space. We evaluate FIRE on an 8-DOF manipulator in five categories of motion planning problems with sensed environments. Our experiments show that FIRE retrieves relevant experiences which can informatively guide sampling-based planners even in problems outside its training distribution, outperforming other baselines.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Random Offset Block Embedding Array (ROBE) for CriteoTB Benchmark MLPerf DLRM Model : 1000$\times$ Compression and 3.1$\times$ Faster Inference

Deep learning for recommendation data is one of the most pervasive and challenging AI workload in recent times. State-of-the-art recommendation models are one of the largest models matching the likes of GPT-3 and Switch Transformer. Challenges in deep learning recommendation models (DLRM) stem from learning dense embeddings for each of the categorical tokens. These embedding tables in industrial scale models can be as large as hundreds of terabytes. Such large models lead to a plethora of engineering challenges, not to mention prohibitive communication overheads, and slower training and inference times. Of these, slower inference time directly impacts user experience. Model compression for DLRM is gaining traction and the community has recently shown impressive compression results. In this paper, we present Random Offset Block Embedding Array (ROBE) as a low memory alternative to embedding tables which provide orders of magnitude reduction in memory usage while maintaining accuracy and boosting execution speed. ROBE is a simple fundamental approach in improving both cache performance and the variance of randomized hashing, which could be of independent interest in itself. We demonstrate that we can successfully train DLRM models with same accuracy while using $1000 \times$ less memory. A $1000\times$ compressed model directly results in faster inference without any engineering effort. In particular, we show that we can train DLRM model using ROBE array of size 100MB on a single GPU to achieve AUC of 0.8025 or higher as required by official MLPerf CriteoTB benchmark DLRM model of 100GB while achieving about $3.1\times$ (209\%) improvement in inference throughput.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

The trade-offs of model size in large recommendation models : A 10000 $\times$ compressed criteo-tb DLRM model (100 GB parameters to mere 10MB)

Embedding tables dominate industrial-scale recommendation model sizes, using up to terabytes of memory. A popular and the largest publicly available machine learning MLPerf benchmark on recommendation data is a Deep Learning Recommendation Model (DLRM) trained on a terabyte of click-through data. It contains 100GB of embedding memory (25+Billion parameters). DLRMs, due to their sheer size and the associated volume of data, face difficulty in training, deploying for inference, and memory bottlenecks due to large embedding tables. This paper analyzes and extensively evaluates a generic parameter sharing setup (PSS) for compressing DLRM models. We show theoretical upper bounds on the learnable memory requirements for achieving $(1 \pm ε)$ approximations to the embedding table. Our bounds indicate exponentially fewer parameters suffice for good accuracy. To this end, we demonstrate a PSS DLRM reaching 10000$\times$ compression on criteo-tb without losing quality. Such a compression, however, comes with a caveat. It requires 4.5 $\times$ more iterations to reach the same saturation quality. The paper argues that this tradeoff needs more investigations as it might be significantly favorable. Leveraging the small size of the compressed model, we show a 4.3$\times$ improvement in training latency leading to similar overall training times. Thus, in the tradeoff between system advantage of a small DLRM model vs. slower convergence, we show that scales are tipped towards having a smaller DLRM model, leading to faster inference, easier deployment, and similar training times.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Beyond Convolutions: A Novel Deep Learning Approach for Raw Seismic Data Ingestion

Traditional seismic processing workflows (SPW) are expensive, requiring over a year of human and computational effort. Deep learning (DL) based data-driven seismic workflows (DSPW) hold the potential to reduce these timelines to a few minutes. Raw seismic data (terabytes) and required subsurface prediction (gigabytes) are enormous. This large-scale, spatially irregular time-series data poses seismic data ingestion (SDI) as an unconventional yet fundamental problem in DSPW. Current DL research is limited to small-scale simplified synthetic datasets as they treat seismic data like images and process them with convolution networks. Real seismic data, however, is at least 5D. Applying 5D convolutions to this scale is computationally prohibitive. Moreover, raw seismic data is highly unstructured and hence inherently non-image like. We propose a fundamental shift to move away from convolutions and introduce SESDI: Set Embedding based SDI approach. SESDI first breaks down the mammoth task of large-scale prediction into an efficient compact auxiliary task. SESDI gracefully incorporates irregularities in data with its novel model architecture. We believe SESDI is the first successful demonstration of end-to-end learning on real seismic data. SESDI achieves SSIM of over 0.8 on velocity inversion task on real proprietary data from the Gulf of Mexico and outperforms the state-of-the-art U-Net model on synthetic datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Density Sketches for Sampling and Estimation

We introduce Density sketches (DS): a succinct online summary of the data distribution. DS can accurately estimate point wise probability density. Interestingly, DS also provides a capability to sample unseen novel data from the underlying data distribution. Thus, analogous to popular generative models, DS allows us to succinctly replace the real-data in almost all machine learning pipelines with synthetic examples drawn from the same distribution as the original data. However, unlike generative models, which do not have any statistical guarantees, DS leads to theoretically sound asymptotically converging consistent estimators of the underlying density function. Density sketches also have many appealing properties making them ideal for large-scale distributed applications. DS construction is an online algorithm. The sketches are additive, i.e., the sum of two sketches is the sketch of the combined data. These properties allow data to be collected from distributed sources, compressed into a density sketch, efficiently transmitted in the sketch form to a central server, merged, and re-sampled into a synthetic database for modeling applications. Thus, density sketches can potentially revolutionize how we store, communicate, and distribute data.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A One-Pass Private Sketch for Most Machine Learning Tasks

Differential privacy (DP) is a compelling privacy definition that explains the privacy-utility tradeoff via formal, provable guarantees. Inspired by recent progress toward general-purpose data release algorithms, we propose a private sketch, or small summary of the dataset, that supports a multitude of machine learning tasks including regression, classification, density estimation, near-neighbor search, and more. Our sketch consists of randomized contingency tables that are indexed with locality-sensitive hashing and constructed with an efficient one-pass algorithm. We prove competitive error bounds for DP kernel density estimation. Existing methods for DP kernel density estimation scale poorly, often exponentially slower with an increase in dimensions. In contrast, our sketch can quickly run on large, high-dimensional datasets in a single pass. Exhaustive experiments show that our generic sketch delivers a similar privacy-utility tradeoff when compared to existing DP methods at a fraction of the computation cost. We expect that our sketch will enable differential privacy in distributed, large-scale machine learning settings.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Angular Visual Hardness

Recent convolutional neural networks (CNNs) have led to impressive performance but often suffer from poor calibration. They tend to be overconfident, with the model confidence not always reflecting the underlying true ambiguity and hardness. In this paper, we propose angular visual hardness (AVH), a score given by the normalized angular distance between the sample feature embedding and the target classifier to measure sample hardness. We validate this score with an in-depth and extensive scientific study, and observe that CNN models with the highest accuracy also have the best AVH scores. This agrees with an earlier finding that state-of-art models improve on the classification of harder examples. We observe that the training dynamics of AVH is vastly different compared to the training loss. Specifically, AVH quickly reaches a plateau for all samples even though the training loss keeps improving. This suggests the need for designing better loss functions that can target harder examples more effectively. We also find that AVH has a statistically significant correlation with human visual hardness. Finally, we demonstrate the benefit of AVH to a variety of applications such as self-training for domain adaptation and domain generalization.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Bloom Origami Assays: Practical Group Testing

We study the problem usually referred to as group testing in the context of COVID-19. Given n samples collected from patients, how should we select and test mixtures of samples to maximize information and minimize the number of tests? Group testing is a well-studied problem with several appealing solutions, but recent biological studies impose practical constraints for COVID-19 that are incompatible with traditional methods. Furthermore, existing methods use unnecessarily restrictive solutions, which were devised for settings with more memory and compute constraints than the problem at hand. This results in poor utility. In the new setting, we obtain strong solutions for small values of n using evolutionary strategies. We then develop a new method combining Bloom filters with belief propagation to scale to larger values of n (more than 100) with good empirical results. We also present a more accurate decoding algorithm that is tailored for specific COVID-19 settings. This work demonstrates the practical gap between dedicated algorithms and well-known generic solutions. Our efforts results in a new and practical multiplex method yielding strong empirical performance without mixing more than a chosen number of patients into the same probe. Finally, we briefly discuss adaptive methods, casting them into the framework of adaptive sub-modularity.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Climbing the WOL: Training for Cheaper Inference

Efficient inference for wide output layers (WOLs) is an essential yet challenging task in large scale machine learning. Most approaches reduce this problem to approximate maximum inner product search (MIPS), which relies heavily on the observation that for a given model, ground truth labels correspond to logits of highest value during full model inference. However, such an assumption is restrictive in practice. In this paper, we argue that approximate MIPS subroutines, despite having sub-linear computation time, are sub-optimal because they are tailored for retrieving large inner products with high recall instead of retrieving the correct labels. With WOL, the labels often have moderate inner products, which makes approximate MIPS more challenging. We propose an alternative problem formulation, called Label Superior Sampling (LSS), where the objective is to tailor the system to ensure retrieval of the correct label. Accordingly, we propose a novel learned hash approach, which is significantly more efficient and sufficient for high inference accuracy than MIPS baselines. Our extensive evaluation indicates that LSS can match or even outperform full inference accuracy with around 5x speed up and 87% energy reduction.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Distributed Tera-Scale Similarity Search with MPI: Provably Efficient Similarity Search over billions without a Single Distance Computation

We present SLASH (Sketched LocAlity Sensitive Hashing), an MPI (Message Passing Interface) based distributed system for approximate similarity search over terabyte scale datasets. SLASH provides a multi-node implementation of the popular LSH (locality sensitive hashing) algorithm, which is generally implemented on a single machine. We show how we can append the LSH algorithm with heavy hitters sketches to provably solve the (high) similarity search problem without a single distance computation. Overall, we mathematically show that, under realistic data assumptions, we can identify the near-neighbor of a given query $q$ in sub-linear ($ \ll O(n)$) number of simple sketch aggregation operations only. To make such a system practical, we offer a novel design and sketching solution to reduce the inter-machine communication overheads exponentially. In a direct comparison on comparable hardware, SLASH is more than 10000x faster than the popular LSH package in PySpark. PySpark is a widely-adopted distributed implementation of the LSH algorithm for large datasets and is deployed in commercial platforms. In the end, we show how our system scale to Tera-scale Criteo dataset with more than 4 billion samples. SLASH can index this 2.3 terabyte data over 20 nodes in under an hour, with query times in a fraction of milliseconds. To the best of our knowledge, there is no open-source system that can index and perform a similarity search on Criteo with a commodity cluster.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints

The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side, especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT solvers, has been remarkable. Yet, while SAT solvers aimed at solving industrial-scale benchmarks in Conjunctive Normal Form (CNF) have become quite mature, SAT solvers that are effective on other types of constraints, e.g., cardinality constraints and XORs, are less well studied; a general approach to handling non-CNF constraints is still lacking. In addition, previous work indicated that for specific classes of benchmarks, the running time of extant SAT solvers depends heavily on properties of the formula and details of encoding, instead of the scale of the benchmarks, which adds uncertainty to expectations of running time. To address the issues above, we design FourierSAT, an incomplete SAT solver based on Fourier analysis of Boolean functions, a technique to represent Boolean functions by multilinear polynomials. By such a reduction to continuous optimization, we propose an algebraic framework for solving systems consisting of different types of constraints. The idea is to leverage gradient information to guide the search process in the direction of local improvements. Empirical results demonstrate that FourierSAT is more robust than other solvers on certain classes of benchmarks.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Privacy Adversarial Network: Representation Learning for Mobile Data Privacy

The remarkable success of machine learning has fostered a growing number of cloud-based intelligent services for mobile users. Such a service requires a user to send data, e.g. image, voice and video, to the provider, which presents a serious challenge to user privacy. To address this, prior works either obfuscate the data, e.g. add noise and remove identity information, or send representations extracted from the data, e.g. anonymized features. They struggle to balance between the service utility and data privacy because obfuscated data reduces utility and extracted representation may still reveal sensitive information. This work departs from prior works in methodology: we leverage adversarial learning to a better balance between privacy and utility. We design a \textit{representation encoder} that generates the feature representations to optimize against the privacy disclosure risk of sensitive information (a measure of privacy) by the \textit{privacy adversaries}, and concurrently optimize with the task inference accuracy (a measure of utility) by the \textit{utility discriminator}. The result is the privacy adversarial network (\systemname), a novel deep model with the new training algorithm, that can automatically learn representations from the raw data. Intuitively, PAN adversarially forces the extracted representations to only convey the information required by the target task. Surprisingly, this constitutes an implicit regularization that actually improves task accuracy. As a result, PAN achieves better utility and better privacy at the same time! We report extensive experiments on six popular datasets and demonstrate the superiority of \systemname compared with alternative methods reported in prior work.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

RAMBO: Repeated And Merged BloOm Filter for Ultra-fast Multiple Set Membership Testing (MSMT) on Large-Scale Data

Multiple Set Membership Testing (MSMT) is a well-known problem in a variety of search and query applications. Given a dataset of K different sets and a query q, it aims to find all of the sets containing the query. Trivially, an MSMT instance can be reduced to K membership testing instances, each with the same q, leading to O(K) query time with a simple array of Bloom Filters. We propose a data-structure called RAMBO (Repeated And Merged BloOm Filter) that achieves O(\sqrt{K} log K) query time in expectation with an additional worst-case memory cost factor of O(log K) beyond the array of Bloom Filters. Due to this, RAMBO is a very fast and accurate data-structure. Apart from being embarrassingly parallel, supporting cheap updates for streaming inputs, zero false-negative rate, and low false-positive rate, RAMBO beats the state-of-the-art approaches for genome indexing methods: COBS (Compact bit-sliced signature index), Sequence Bloom Trees (a Bloofi based implementation), HowDeSBT, SSBT, and document indexing methods like BitFunnel. The proposed data-structure is simply a count-min sketch type arrangement of a membership testing utility (Bloom Filter in our case). It indexes k-grams and provides an approximate membership testing based search utility. The simplicity of the algorithm and embarrassingly parallel architecture allows us to index a 170 TB genome dataset in a mere 14 hours on a cluster of 100 nodes while competing methods require weeks.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Revisiting Consistent Hashing with Bounded Loads

Dynamic load balancing lies at the heart of distributed caching. Here, the goal is to assign objects (load) to servers (computing nodes) in a way that provides load balancing while at the same time dynamically adjusts to the addition or removal of servers. One essential requirement is that the addition or removal of small servers should not require us to recompute the complete assignment. A popular and widely adopted solution is the two-decade-old Consistent Hashing (CH). Recently, an elegant extension was provided to account for server bounds. In this paper, we identify that existing methodologies for CH and its variants suffer from cascaded overflow, leading to poor load balancing. This cascading effect leads to decreasing performance of the hashing procedure with increasing load. To overcome the cascading effect, we propose a simple solution to CH based on recent advances in fast minwise hashing. We show, both theoretically and empirically, that our proposed solution is significantly superior for load balancing and is optimal in many senses. On the AOL search dataset and Indiana University Clicks dataset with real user activity, our proposed solution reduces cache misses by several magnitudes.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

SDM-Net: A Simple and Effective Model for Generalized Zero-Shot Learning

Zero-Shot Learning (ZSL) is a classification task where we do not have even a single training labeled example from a set of unseen classes. Instead, we only have prior information (or description) about seen and unseen classes, often in the form of physically realizable or descriptive attributes. Lack of any single training example from a set of classes prohibits use of standard classification techniques and losses, including the popular crossentropy loss. Currently, state-of-the-art approaches encode the prior class information into dense vectors and optimize some distance between the learned projections of the input vector and the corresponding class vector (collectively known as embedding models). In this paper, we propose a novel architecture of casting zero-shot learning as a standard neural-network with crossentropy loss. During training our approach performs soft-labeling by combining the observed training data for the seen classes with the similarity information from the attributes for which we have no training data or unseen classes. To the best of our knowledge, such similarity based soft-labeling is not explored in the field of deep learning. We evaluate the proposed model on the four benchmark datasets for zero-shot learning, AwA, aPY, SUN and CUB datasets, and show that our model achieves significant improvement over the state-of-the-art methods in Generalized-ZSL and ZSL settings on all of these datasets consistently.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

SLIDE : In Defense of Smart Algorithms over Hardware Acceleration for Large-Scale Deep Learning Systems

Deep Learning (DL) algorithms are the central focus of modern machine learning systems. As data volumes keep growing, it has become customary to train large neural networks with hundreds of millions of parameters to maintain enough capacity to memorize these volumes and obtain state-of-the-art accuracy. To get around the costly computations associated with large models and data, the community is increasingly investing in specialized hardware for model training. However, specialized hardware is expensive and hard to generalize to a multitude of tasks. The progress on the algorithmic front has failed to demonstrate a direct advantage over powerful hardware such as NVIDIA-V100 GPUs. This paper provides an exception. We propose SLIDE (Sub-LInear Deep learning Engine) that uniquely blends smart randomized algorithms, with multi-core parallelism and workload optimization. Using just a CPU, SLIDE drastically reduces the computations during both training and inference outperforming an optimized implementation of Tensorflow (TF) on the best available GPU. Our evaluations on industry-scale recommendation datasets, with large fully connected architectures, show that training with SLIDE on a 44 core CPU is more than 3.5 times (1 hour vs. 3.5 hours) faster than the same network trained using TF on Tesla V100 at any given accuracy level. On the same CPU hardware, SLIDE is over 10x faster than TF. We provide codes and scripts for reproducibility.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

SOLAR: Sparse Orthogonal Learned and Random Embeddings

Dense embedding models are commonly deployed in commercial search engines, wherein all the document vectors are pre-computed, and near-neighbor search (NNS) is performed with the query vector to find relevant documents. However, the bottleneck of indexing a large number of dense vectors and performing an NNS hurts the query time and accuracy of these models. In this paper, we argue that high-dimensional and ultra-sparse embedding is a significantly superior alternative to dense low-dimensional embedding for both query efficiency and accuracy. Extreme sparsity eliminates the need for NNS by replacing them with simple lookups, while its high dimensionality ensures that the embeddings are informative even when sparse. However, learning extremely high dimensional embeddings leads to blow up in the model size. To make the training feasible, we propose a partitioning algorithm that learns such high dimensional embeddings across multiple GPUs without any communication. This is facilitated by our novel asymmetric mixture of Sparse, Orthogonal, Learned and Random (SOLAR) Embeddings. The label vectors are random, sparse, and near-orthogonal by design, while the query vectors are learned and sparse. We theoretically prove that our way of one-sided learning is equivalent to learning both query and label embeddings. With these unique properties, we can successfully train 500K dimensional SOLAR embeddings for the tasks of searching through 1.6M books and multi-label classification on the three largest public datasets. We achieve superior precision and recall compared to the respective state-of-the-art baselines for each of the tasks with up to 10 times faster speed.

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preprint2020arXiv

STORM: Foundations of End-to-End Empirical Risk Minimization on the Edge

Empirical risk minimization is perhaps the most influential idea in statistical learning, with applications to nearly all scientific and technical domains in the form of regression and classification models. To analyze massive streaming datasets in distributed computing environments, practitioners increasingly prefer to deploy regression models on edge rather than in the cloud. By keeping data on edge devices, we minimize the energy, communication, and data security risk associated with the model. Although it is equally advantageous to train models at the edge, a common assumption is that the model was originally trained in the cloud, since training typically requires substantial computation and memory. To this end, we propose STORM, an online sketch for empirical risk minimization. STORM compresses a data stream into a tiny array of integer counters. This sketch is sufficient to estimate a variety of surrogate losses over the original dataset. We provide rigorous theoretical analysis and show that STORM can estimate a carefully chosen surrogate loss for the least-squares objective. In an exhaustive experimental comparison for linear regression models on real-world datasets, we find that STORM allows accurate regression models to be trained.

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preprint2020arXiv

Sub-linear Memory Sketches for Near Neighbor Search on Streaming Data

We present the first sublinear memory sketch that can be queried to find the nearest neighbors in a dataset. Our online sketching algorithm compresses an N element dataset to a sketch of size $O(N^b \log^3 N)$ in $O(N^{(b+1)} \log^3 N)$ time, where $b < 1$. This sketch can correctly report the nearest neighbors of any query that satisfies a stability condition parameterized by $b$. We achieve sublinear memory performance on stable queries by combining recent advances in locality sensitive hash (LSH)-based estimators, online kernel density estimation, and compressed sensing. Our theoretical results shed new light on the memory-accuracy tradeoff for nearest neighbor search, and our sketch, which consists entirely of short integer arrays, has a variety of attractive features in practice. We evaluate the memory-recall tradeoff of our method on a friend recommendation task in the Google Plus social media network. We obtain orders of magnitude better compression than the random projection based alternative while retaining the ability to report the nearest neighbors of practical queries.

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preprint2016arXiv

2-Bit Random Projections, NonLinear Estimators, and Approximate Near Neighbor Search

The method of random projections has become a standard tool for machine learning, data mining, and search with massive data at Web scale. The effective use of random projections requires efficient coding schemes for quantizing (real-valued) projected data into integers. In this paper, we focus on a simple 2-bit coding scheme. In particular, we develop accurate nonlinear estimators of data similarity based on the 2-bit strategy. This work will have important practical applications. For example, in the task of near neighbor search, a crucial step (often called re-ranking) is to compute or estimate data similarities once a set of candidate data points have been identified by hash table techniques. This re-ranking step can take advantage of the proposed coding scheme and estimator. As a related task, in this paper, we also study a simple uniform quantization scheme for the purpose of building hash tables with projected data. Our analysis shows that typically only a small number of bits are needed. For example, when the target similarity level is high, 2 or 3 bits might be sufficient. When the target similarity level is not so high, it is preferable to use only 1 or 2 bits. Therefore, a 2-bit scheme appears to be overall a good choice for the task of sublinear time approximate near neighbor search via hash tables. Combining these results, we conclude that 2-bit random projections should be recommended for approximate near neighbor search and similarity estimation. Extensive experimental results are provided.

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preprint2016arXiv

Exact Weighted Minwise Hashing in Constant Time

Weighted minwise hashing (WMH) is one of the fundamental subroutine, required by many celebrated approximation algorithms, commonly adopted in industrial practice for large scale-search and learning. The resource bottleneck of the algorithms is the computation of multiple (typically a few hundreds to thousands) independent hashes of the data. The fastest hashing algorithm is by Ioffe \cite{Proc:Ioffe_ICDM10}, which requires one pass over the entire data vector, $O(d)$ ($d$ is the number of non-zeros), for computing one hash. However, the requirement of multiple hashes demands hundreds or thousands passes over the data. This is very costly for modern massive dataset. In this work, we break this expensive barrier and show an expected constant amortized time algorithm which computes $k$ independent and unbiased WMH in time $O(k)$ instead of $O(dk)$ required by Ioffe's method. Moreover, our proposal only needs a few bits (5 - 9 bits) of storage per hash value compared to around $64$ bits required by the state-of-art-methodologies. Experimental evaluations, on real datasets, show that for computing 500 WMH, our proposal can be 60000x faster than the Ioffe's method without losing any accuracy. Our method is also around 100x faster than approximate heuristics capitalizing on the efficient "densified" one permutation hashing schemes \cite{Proc:OneHashLSH_ICML14}. Given the simplicity of our approach and its significant advantages, we hope that it will replace existing implementations in practice.

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preprint2016arXiv

Near-Isometric Binary Hashing for Large-scale Datasets

We develop a scalable algorithm to learn binary hash codes for indexing large-scale datasets. Near-isometric binary hashing (NIBH) is a data-dependent hashing scheme that quantizes the output of a learned low-dimensional embedding to obtain a binary hash code. In contrast to conventional hashing schemes, which typically rely on an $\ell_2$-norm (i.e., average distortion) minimization, NIBH is based on a $\ell_{\infty}$-norm (i.e., worst-case distortion) minimization that provides several benefits, including superior distance, ranking, and near-neighbor preservation performance. We develop a practical and efficient algorithm for NIBH based on column generation that scales well to large datasets. A range of experimental evaluations demonstrate the superiority of NIBH over ten state-of-the-art binary hashing schemes.

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preprint2016arXiv

Scalable and Sustainable Deep Learning via Randomized Hashing

Current deep learning architectures are growing larger in order to learn from complex datasets. These architectures require giant matrix multiplication operations to train millions of parameters. Conversely, there is another growing trend to bring deep learning to low-power, embedded devices. The matrix operations, associated with both training and testing of deep networks, are very expensive from a computational and energy standpoint. We present a novel hashing based technique to drastically reduce the amount of computation needed to train and test deep networks. Our approach combines recent ideas from adaptive dropouts and randomized hashing for maximum inner product search to select the nodes with the highest activation efficiently. Our new algorithm for deep learning reduces the overall computational cost of forward and back-propagation by operating on significantly fewer (sparse) nodes. As a consequence, our algorithm uses only 5% of the total multiplications, while keeping on average within 1% of the accuracy of the original model. A unique property of the proposed hashing based back-propagation is that the updates are always sparse. Due to the sparse gradient updates, our algorithm is ideally suited for asynchronous and parallel training leading to near linear speedup with increasing number of cores. We demonstrate the scalability and sustainability (energy efficiency) of our proposed algorithm via rigorous experimental evaluations on several real datasets.

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preprint2016arXiv

SSH (Sketch, Shingle, & Hash) for Indexing Massive-Scale Time Series

Similarity search on time series is a frequent operation in large-scale data-driven applications. Sophisticated similarity measures are standard for time series matching, as they are usually misaligned. Dynamic Time Warping or DTW is the most widely used similarity measure for time series because it combines alignment and matching at the same time. However, the alignment makes DTW slow. To speed up the expensive similarity search with DTW, branch and bound based pruning strategies are adopted. However, branch and bound based pruning are only useful for very short queries (low dimensional time series), and the bounds are quite weak for longer queries. Due to the loose bounds branch and bound pruning strategy boils down to a brute-force search. To circumvent this issue, we design SSH (Sketch, Shingle, & Hashing), an efficient and approximate hashing scheme which is much faster than the state-of-the-art branch and bound searching technique: the UCR suite. SSH uses a novel combination of sketching, shingling and hashing techniques to produce (probabilistic) indexes which align (near perfectly) with DTW similarity measure. The generated indexes are then used to create hash buckets for sub-linear search. Our results show that SSH is very effective for longer time sequence and prunes around 95% candidates, leading to the massive speedup in search with DTW. Empirical results on two large-scale benchmark time series data show that our proposed method can be around 20 times faster than the state-of-the-art package (UCR suite) without any significant loss in accuracy.

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preprint2015arXiv

Blocking Methods Applied to Casualty Records from the Syrian Conflict

Estimation of death counts and associated standard errors is of great importance in armed conflict such as the ongoing violence in Syria, as well as historical conflicts in Guatemala, Perú, Colombia, Timor Leste, and Kosovo. For example, statistical estimates of death counts were cited as important evidence in the trial of General Efraín Ríos Montt for acts of genocide in Guatemala. Estimation relies on both record linkage and multiple systems estimation. A key first step in this process is identifying ways to partition the records such that they are computationally manageable. This step is referred to as blocking and is a major challenge for the Syrian database since it is sparse in the number of duplicate records and feature poor in its attributes. As a consequence, we propose locality sensitive hashing (LSH) methods to overcome these challenges. We demonstrate the computational superiority and error rates of these methods by comparing our proposed approach with others in the literature. We conclude with a discussion of many challenges of merging LSH with record linkage to achieve an estimate of the number of uniquely documented deaths in the Syrian conflict.

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preprint2014arXiv

A New Space for Comparing Graphs

Finding a new mathematical representations for graph, which allows direct comparison between different graph structures, is an open-ended research direction. Having such a representation is the first prerequisite for a variety of machine learning algorithms like classification, clustering, etc., over graph datasets. In this paper, we propose a symmetric positive semidefinite matrix with the $(i,j)$-{th} entry equal to the covariance between normalized vectors $A^ie$ and $A^je$ ($e$ being vector of all ones) as a representation for graph with adjacency matrix $A$. We show that the proposed matrix representation encodes the spectrum of the underlying adjacency matrix and it also contains information about the counts of small sub-structures present in the graph such as triangles and small paths. In addition, we show that this matrix is a \emph{"graph invariant"}. All these properties make the proposed matrix a suitable object for representing graphs. The representation, being a covariance matrix in a fixed dimensional metric space, gives a mathematical embedding for graphs. This naturally leads to a measure of similarity on graph objects. We define similarity between two given graphs as a Bhattacharya similarity measure between their corresponding covariance matrix representations. As shown in our experimental study on the task of social network classification, such a similarity measure outperforms other widely used state-of-the-art methodologies. Our proposed method is also computationally efficient. The computation of both the matrix representation and the similarity value can be performed in operations linear in the number of edges. This makes our method scalable in practice. We believe our theoretical and empirical results provide evidence for studying truncated power iterations, of the adjacency matrix, to characterize social networks.

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preprint2014arXiv

Asymmetric LSH (ALSH) for Sublinear Time Maximum Inner Product Search (MIPS)

We present the first provably sublinear time algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Our proposal is also the first hashing algorithm for searching with (un-normalized) inner product as the underlying similarity measure. Finding hashing schemes for MIPS was considered hard. We formally show that the existing Locality Sensitive Hashing (LSH) framework is insufficient for solving MIPS, and then we extend the existing LSH framework to allow asymmetric hashing schemes. Our proposal is based on an interesting mathematical phenomenon in which inner products, after independent asymmetric transformations, can be converted into the problem of approximate near neighbor search. This key observation makes efficient sublinear hashing scheme for MIPS possible. In the extended asymmetric LSH (ALSH) framework, we provide an explicit construction of provably fast hashing scheme for MIPS. The proposed construction and the extended LSH framework could be of independent theoretical interest. Our proposed algorithm is simple and easy to implement. We evaluate the method, for retrieving inner products, in the collaborative filtering task of item recommendations on Netflix and Movielens datasets.

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preprint2014arXiv

Asymmetric Minwise Hashing

Minwise hashing (Minhash) is a widely popular indexing scheme in practice. Minhash is designed for estimating set resemblance and is known to be suboptimal in many applications where the desired measure is set overlap (i.e., inner product between binary vectors) or set containment. Minhash has inherent bias towards smaller sets, which adversely affects its performance in applications where such a penalization is not desirable. In this paper, we propose asymmetric minwise hashing (MH-ALSH), to provide a solution to this problem. The new scheme utilizes asymmetric transformations to cancel the bias of traditional minhash towards smaller sets, making the final "collision probability" monotonic in the inner product. Our theoretical comparisons show that for the task of retrieving with binary inner products asymmetric minhash is provably better than traditional minhash and other recently proposed hashing algorithms for general inner products. Thus, we obtain an algorithmic improvement over existing approaches in the literature. Experimental evaluations on four publicly available high-dimensional datasets validate our claims and the proposed scheme outperforms, often significantly, other hashing algorithms on the task of near neighbor retrieval with set containment. Our proposal is simple and easy to implement in practice.

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preprint2014arXiv

Coding for Random Projections and Approximate Near Neighbor Search

This technical note compares two coding (quantization) schemes for random projections in the context of sub-linear time approximate near neighbor search. The first scheme is based on uniform quantization while the second scheme utilizes a uniform quantization plus a uniformly random offset (which has been popular in practice). The prior work compared the two schemes in the context of similarity estimation and training linear classifiers, with the conclusion that the step of random offset is not necessary and may hurt the performance (depending on the similarity level). The task of near neighbor search is related to similarity estimation with importance distinctions and requires own study. In this paper, we demonstrate that in the context of near neighbor search, the step of random offset is not needed either and may hurt the performance (sometimes significantly so, depending on the similarity and other parameters).

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preprint2014arXiv

Graph Kernels via Functional Embedding

We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any reordering of the vertices. This property eliminates the difficulty of handling exponentially many isomorphic forms. Bhattacharyya kernel constructed between these functionals significantly outperforms the state-of-the-art graph kernels on 3 out of the 4 standard benchmark graph classification datasets, demonstrating the superiority of our approach. The proposed methodology is simple and runs in time linear in the number of edges, which makes our kernel more efficient and scalable compared to many widely adopted graph kernels with running time cubic in the number of vertices.

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preprint2014arXiv

Improved Asymmetric Locality Sensitive Hashing (ALSH) for Maximum Inner Product Search (MIPS)

Recently it was shown that the problem of Maximum Inner Product Search (MIPS) is efficient and it admits provably sub-linear hashing algorithms. Asymmetric transformations before hashing were the key in solving MIPS which was otherwise hard. In the prior work, the authors use asymmetric transformations which convert the problem of approximate MIPS into the problem of approximate near neighbor search which can be efficiently solved using hashing. In this work, we provide a different transformation which converts the problem of approximate MIPS into the problem of approximate cosine similarity search which can be efficiently solved using signed random projections. Theoretical analysis show that the new scheme is significantly better than the original scheme for MIPS. Experimental evaluations strongly support the theoretical findings.

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preprint2014arXiv

Improved Densification of One Permutation Hashing

The existing work on densification of one permutation hashing reduces the query processing cost of the $(K,L)$-parameterized Locality Sensitive Hashing (LSH) algorithm with minwise hashing, from $O(dKL)$ to merely $O(d + KL)$, where $d$ is the number of nonzeros of the data vector, $K$ is the number of hashes in each hash table, and $L$ is the number of hash tables. While that is a substantial improvement, our analysis reveals that the existing densification scheme is sub-optimal. In particular, there is no enough randomness in that procedure, which affects its accuracy on very sparse datasets. In this paper, we provide a new densification procedure which is provably better than the existing scheme. This improvement is more significant for very sparse datasets which are common over the web. The improved technique has the same cost of $O(d + KL)$ for query processing, thereby making it strictly preferable over the existing procedure. Experimental evaluations on public datasets, in the task of hashing based near neighbor search, support our theoretical findings.

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preprint2014arXiv

In Defense of MinHash Over SimHash

MinHash and SimHash are the two widely adopted Locality Sensitive Hashing (LSH) algorithms for large-scale data processing applications. Deciding which LSH to use for a particular problem at hand is an important question, which has no clear answer in the existing literature. In this study, we provide a theoretical answer (validated by experiments) that MinHash virtually always outperforms SimHash when the data are binary, as common in practice such as search. The collision probability of MinHash is a function of resemblance similarity ($\mathcal{R}$), while the collision probability of SimHash is a function of cosine similarity ($\mathcal{S}$). To provide a common basis for comparison, we evaluate retrieval results in terms of $\mathcal{S}$ for both MinHash and SimHash. This evaluation is valid as we can prove that MinHash is a valid LSH with respect to $\mathcal{S}$, by using a general inequality $\mathcal{S}^2\leq \mathcal{R}\leq \frac{\mathcal{S}}{2-\mathcal{S}}$. Our worst case analysis can show that MinHash significantly outperforms SimHash in high similarity region. Interestingly, our intensive experiments reveal that MinHash is also substantially better than SimHash even in datasets where most of the data points are not too similar to each other. This is partly because, in practical data, often $\mathcal{R}\geq \frac{\mathcal{S}}{z-\mathcal{S}}$ holds where $z$ is only slightly larger than 2 (e.g., $z\leq 2.1$). Our restricted worst case analysis by assuming $\frac{\mathcal{S}}{z-\mathcal{S}}\leq \mathcal{R}\leq \frac{\mathcal{S}}{2-\mathcal{S}}$ shows that MinHash indeed significantly outperforms SimHash even in low similarity region. We believe the results in this paper will provide valuable guidelines for search in practice, especially when the data are sparse.

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preprint2013arXiv

Coding for Random Projections

The method of random projections has become very popular for large-scale applications in statistical learning, information retrieval, bio-informatics and other applications. Using a well-designed coding scheme for the projected data, which determines the number of bits needed for each projected value and how to allocate these bits, can significantly improve the effectiveness of the algorithm, in storage cost as well as computational speed. In this paper, we study a number of simple coding schemes, focusing on the task of similarity estimation and on an application to training linear classifiers. We demonstrate that uniform quantization outperforms the standard existing influential method (Datar et. al. 2004). Indeed, we argue that in many cases coding with just a small number of bits suffices. Furthermore, we also develop a non-uniform 2-bit coding scheme that generally performs well in practice, as confirmed by our experiments on training linear support vector machines (SVM).

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preprint2012arXiv

b-Bit Minwise Hashing in Practice: Large-Scale Batch and Online Learning and Using GPUs for Fast Preprocessing with Simple Hash Functions

In this paper, we study several critical issues which must be tackled before one can apply b-bit minwise hashing to the volumes of data often used industrial applications, especially in the context of search. 1. (b-bit) Minwise hashing requires an expensive preprocessing step that computes k (e.g., 500) minimal values after applying the corresponding permutations for each data vector. We developed a parallelization scheme using GPUs and observed that the preprocessing time can be reduced by a factor of 20-80 and becomes substantially smaller than the data loading time. 2. One major advantage of b-bit minwise hashing is that it can substantially reduce the amount of memory required for batch learning. However, as online algorithms become increasingly popular for large-scale learning in the context of search, it is not clear if b-bit minwise yields significant improvements for them. This paper demonstrates that $b$-bit minwise hashing provides an effective data size/dimension reduction scheme and hence it can dramatically reduce the data loading time for each epoch of the online training process. This is significant because online learning often requires many (e.g., 10 to 100) epochs to reach a sufficient accuracy. 3. Another critical issue is that for very large data sets it becomes impossible to store a (fully) random permutation matrix, due to its space requirements. Our paper is the first study to demonstrate that $b$-bit minwise hashing implemented using simple hash functions, e.g., the 2-universal (2U) and 4-universal (4U) hash families, can produce very similar learning results as using fully random permutations. Experiments on datasets of up to 200GB are presented.

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preprint2011arXiv

Hashing Algorithms for Large-Scale Learning

In this paper, we first demonstrate that b-bit minwise hashing, whose estimators are positive definite kernels, can be naturally integrated with learning algorithms such as SVM and logistic regression. We adopt a simple scheme to transform the nonlinear (resemblance) kernel into linear (inner product) kernel; and hence large-scale problems can be solved extremely efficiently. Our method provides a simple effective solution to large-scale learning in massive and extremely high-dimensional datasets, especially when data do not fit in memory. We then compare b-bit minwise hashing with the Vowpal Wabbit (VW) algorithm (which is related the Count-Min (CM) sketch). Interestingly, VW has the same variances as random projections. Our theoretical and empirical comparisons illustrate that usually $b$-bit minwise hashing is significantly more accurate (at the same storage) than VW (and random projections) in binary data. Furthermore, $b$-bit minwise hashing can be combined with VW to achieve further improvements in terms of training speed, especially when $b$ is large.

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preprint2011arXiv

Training Logistic Regression and SVM on 200GB Data Using b-Bit Minwise Hashing and Comparisons with Vowpal Wabbit (VW)

We generated a dataset of 200 GB with 10^9 features, to test our recent b-bit minwise hashing algorithms for training very large-scale logistic regression and SVM. The results confirm our prior work that, compared with the VW hashing algorithm (which has the same variance as random projections), b-bit minwise hashing is substantially more accurate at the same storage. For example, with merely 30 hashed values per data point, b-bit minwise hashing can achieve similar accuracies as VW with 2^14 hashed values per data point. We demonstrate that the preprocessing cost of b-bit minwise hashing is roughly on the same order of magnitude as the data loading time. Furthermore, by using a GPU, the preprocessing cost can be reduced to a small fraction of the data loading time. Minwise hashing has been widely used in industry, at least in the context of search. One reason for its popularity is that one can efficiently simulate permutations by (e.g.,) universal hashing. In other words, there is no need to store the permutation matrix. In this paper, we empirically verify this practice, by demonstrating that even using the simplest 2-universal hashing does not degrade the learning performance.

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