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preprint2020arXiv

Customized Graph Embedding: Tailoring Embedding Vectors to different Applications

Graph is a natural representation of data for a variety of real-word applications, such as knowledge graph mining, social network analysis and biological network comparison. For these applications, graph embedding is crucial as it provides vector representations of the graph. One limitation of existing graph embedding methods is that their embedding optimization procedures are disconnected from the target application. In this paper, we propose a novel approach, namely Customized Graph Embedding (CGE) to tackle this problem. The CGE algorithm learns customized vector representations of graph nodes by differentiating the importance of distinct graph paths automatically for a specific application. Extensive experiments were carried out on a diverse set of node classification datasets, which demonstrate strong performances of CGE and provide deep insights into the model.

preprint2021arXiv

Highly Efficient Knowledge Graph Embedding Learning with Orthogonal Procrustes Analysis

Knowledge Graph Embeddings (KGEs) have been intensively explored in recent years due to their promise for a wide range of applications. However, existing studies focus on improving the final model performance without acknowledging the computational cost of the proposed approaches, in terms of execution time and environmental impact. This paper proposes a simple yet effective KGE framework which can reduce the training time and carbon footprint by orders of magnitudes compared with state-of-the-art approaches, while producing competitive performance. We highlight three technical innovations: full batch learning via relational matrices, closed-form Orthogonal Procrustes Analysis for KGEs, and non-negative-sampling training. In addition, as the first KGE method whose entity embeddings also store full relation information, our trained models encode rich semantics and are highly interpretable. Comprehensive experiments and ablation studies involving 13 strong baselines and two standard datasets verify the effectiveness and efficiency of our algorithm.

preprint2021arXiv

A Mask R-CNN approach to counting bacterial colony forming units in pharmaceutical development

We present an application of the well-known Mask R-CNN approach to the counting of different types of bacterial colony forming units that were cultured in Petri dishes. Our model was made available to lab technicians in a modern SPA (Single-Page Application). Users can upload images of dishes, after which the Mask R-CNN model that was trained and tuned specifically for this task detects the number of BVG- and BVG+ colonies and displays these in an interactive interface for the user to verify. Users can then check the model's predictions, correct them if deemed necessary, and finally validate them. Our adapted Mask R-CNN model achieves a mean average precision (mAP) of 94\% at an intersection-over-union (IoU) threshold of 50\%. With these encouraging results, we see opportunities to bring the benefits of improved accuracy and time saved to related problems, such as generalising to other bacteria types and viral foci counting.

preprint2020arXiv

Accurate, Efficient and Scalable Graph Embedding

The Graph Convolutional Network (GCN) model and its variants are powerful graph embedding tools for facilitating classification and clustering on graphs. However, a major challenge is to reduce the complexity of layered GCNs and make them parallelizable and scalable on very large graphs -- state-of the art techniques are unable to achieve scalability without losing accuracy and efficiency. In this paper, we propose novel parallelization techniques for graph sampling-based GCNs that achieve superior scalable performance on very large graphs without compromising accuracy. Specifically, our GCN guarantees work-efficient training and produces order of magnitude savings in computation and communication. To scale GCN training on tightly-coupled shared memory systems, we develop parallelization strategies for the key steps in training: For the graph sampling step, we exploit parallelism within and across multiple sampling instances, and devise an efficient data structure for concurrent accesses that provides theoretical guarantee of near-linear speedup with number of processing units. For the feature propagation step within the sampled graph, we improve cache utilization and reduce DRAM c

preprint2023arXiv

Federated Two Stage Decoupling With Adaptive Personalization Layers

Federated learning has gained significant attention due to its groundbreaking ability to enable distributed learning while maintaining privacy constraints. However, as a consequence of data heterogeneity among decentralized devices, it inherently experiences significant learning degradation and slow convergence speed. Therefore, it is natural to employ the concept of clustering homogeneous clients into the same group, allowing only the model weights within each group to be aggregated. While most existing clustered federated learning methods employ either model gradients or inference outputs as metrics for client partitioning, with the goal of grouping similar devices together, may still have heterogeneity within each cluster. Moreover, there is a scarcity of research exploring the underlying reasons for determining the appropriate timing for clustering, resulting in the common practice of assigning each client to its own individual cluster, particularly in the context of highly non independent and identically distributed (Non-IID) data. In this paper, we introduce a two-stage decoupling federated learning algorithm with adaptive personalization layers named FedTSDP, where client clustering is performed twice according to inference outputs and model weights, respectively. Hopkins amended sampling is adopted to determine the appropriate timing for clustering and the sampling weight of public unlabeled data. In addition, a simple yet effective approach is developed to adaptively adjust the personalization layers based on varying degrees of data skew. Experimental results show that our proposed method has reliable performance on both IID and non-IID scenarios.

preprint2013arXiv

An Unsupervised Feature Learning Approach to Improve Automatic Incident Detection

Sophisticated automatic incident detection (AID) technology plays a key role in contemporary transportation systems. Though many papers were devoted to study incident classification algorithms, few study investigated how to enhance feature representation of incidents to improve AID performance. In this paper, we propose to use an unsupervised feature learning algorithm to generate higher level features to represent incidents. We used real incident data in the experiments and found that effective feature mapping function can be learnt from the data crosses the test sites. With the enhanced features, detection rate (DR), false alarm rate (FAR) and mean time to detect (MTTD) are significantly improved in all of the three representative cases. This approach also provides an alternative way to reduce the amount of labeled data, which is expensive to obtain, required in training better incident classifiers since the feature learning is unsupervised.

preprint2022arXiv

Why Adversarial Training of ReLU Networks Is Difficult?

This paper mathematically derives an analytic solution of the adversarial perturbation on a ReLU network, and theoretically explains the difficulty of adversarial training. Specifically, we formulate the dynamics of the adversarial perturbation generated by the multi-step attack, which shows that the adversarial perturbation tends to strengthen eigenvectors corresponding to a few top-ranked eigenvalues of the Hessian matrix of the loss w.r.t. the input. We also prove that adversarial training tends to strengthen the influence of unconfident input samples with large gradient norms in an exponential manner. Besides, we find that adversarial training strengthens the influence of the Hessian matrix of the loss w.r.t. network parameters, which makes the adversarial training more likely to oscillate along directions of a few samples, and boosts the difficulty of adversarial training. Crucially, our proofs provide a unified explanation for previous findings in understanding adversarial training.

preprint2021arXiv

Counterfactual Representation Learning with Balancing Weights

A key to causal inference with observational data is achieving balance in predictive features associated with each treatment type. Recent literature has explored representation learning to achieve this goal. In this work, we discuss the pitfalls of these strategies - such as a steep trade-off between achieving balance and predictive power - and present a remedy via the integration of balancing weights in causal learning. Specifically, we theoretically link balance to the quality of propensity estimation, emphasize the importance of identifying a proper target population, and elaborate on the complementary roles of feature balancing and weight adjustments. Using these concepts, we then develop an algorithm for flexible, scalable and accurate estimation of causal effects. Finally, we show how the learned weighted representations may serve to facilitate alternative causal learning procedures with appealing statistical features. We conduct an extensive set of experiments on both synthetic examples and standard benchmarks, and report encouraging results relative to state-of-the-art baselines.

preprint2020arXiv

A General Framework for Consistent Structured Prediction with Implicit Loss Embeddings

We propose and analyze a novel theoretical and algorithmic framework for structured prediction. While so far the term has referred to discrete output spaces, here we consider more general settings, such as manifolds or spaces of probability measures. We define structured prediction as a problem where the output space lacks a vectorial structure. We identify and study a large class of loss functions that implicitly defines a suitable geometry on the problem. The latter is the key to develop an algorithmic framework amenable to a sharp statistical analysis and yielding efficient computations. When dealing with output spaces with infinite cardinality, a suitable implicit formulation of the estimator is shown to be crucial.

preprint2022arXiv

Rethinking ValueDice: Does It Really Improve Performance?

Since the introduction of GAIL, adversarial imitation learning (AIL) methods attract lots of research interests. Among these methods, ValueDice has achieved significant improvements: it beats the classical approach Behavioral Cloning (BC) under the offline setting, and it requires fewer interactions than GAIL under the online setting. Are these improvements benefited from more advanced algorithm designs? We answer this question by the following conclusions. First, we show that ValueDice could reduce to BC under the offline setting. Second, we verify that overfitting exists and regularization matters in the low-data regime. Specifically, we demonstrate that with weight decay, BC also nearly matches the expert performance as ValueDice does. The first two claims explain the superior offline performance of ValueDice. Third, we establish that ValueDice does not work when the expert trajectory is subsampled. Instead, the mentioned success of ValueDice holds when the expert trajectory is complete, in which ValueDice is closely related to BC that performs well as mentioned. Finally, we discuss the implications of our research for imitation learning studies beyond ValueDice.

preprint2026arXiv

The Symmetries of Three-Layer ReLU Networks

We develop a framework for analyzing parameter symmetries in deep ReLU networks and obtain a complete characterization of the generic parameter fibers for three-layer bottleneck architectures. Our approach provides explicit semi-algebraic descriptions of these fibers and yields a polynomial time algorithm for deciding functional equivalence of two parameters. The symmetries include discrete and continuous transformations arising from layer composition, and depend on whether deeper layers hide or preserve geometric structure from preceding layers. Finally, we show that some of these symmetries induce local conservation laws along gradient flow, while others do not.

preprint2020arXiv

On the Discrepancy between Density Estimation and Sequence Generation

Many sequence-to-sequence generation tasks, including machine translation and text-to-speech, can be posed as estimating the density of the output y given the input x: p(y|x). Given this interpretation, it is natural to evaluate sequence-to-sequence models using conditional log-likelihood on a test set. However, the goal of sequence-to-sequence generation (or structured prediction) is to find the best output y^ given an input x, and each task has its own downstream metric R that scores a model output by comparing against a set of references y*: R(y^, y* | x). While we hope that a model that excels in density estimation also performs well on the downstream metric, the exact correlation has not been studied for sequence generation tasks. In this paper, by comparing several density estimators on five machine translation tasks, we find that the correlation between rankings of models based on log-likelihood and BLEU varies significantly depending on the range of the model families being compared. First, log-likelihood is highly correlated with BLEU when we consider models within the same family (e.g. autoregressive models, or latent variable models with the same parameterization of the

preprint2016arXiv

Local Discriminant Hyperalignment for multi-subject fMRI data alignment

Multivariate Pattern (MVP) classification can map different cognitive states to the brain tasks. One of the main challenges in MVP analysis is validating the generated results across subjects. However, analyzing multi-subject fMRI data requires accurate functional alignments between neuronal activities of different subjects, which can rapidly increase the performance and robustness of the final results. Hyperalignment (HA) is one of the most effective functional alignment methods, which can be mathematically formulated by the Canonical Correlation Analysis (CCA) methods. Since HA mostly uses the unsupervised CCA techniques, its solution may not be optimized for MVP analysis. By incorporating the idea of Local Discriminant Analysis (LDA) into CCA, this paper proposes Local Discriminant Hyperalignment (LDHA) as a novel supervised HA method, which can provide better functional alignment for MVP analysis. Indeed, the locality is defined based on the stimuli categories in the train-set, where the correlation between all stimuli in the same category will be maximized and the correlation between distinct categories of stimuli approaches to near zero. Experimental studies on multi-subject

preprint2013arXiv

Optimization for Compressed Sensing: the Simplex Method and Kronecker Sparsification

In this paper we present two new approaches to efficiently solve large-scale compressed sensing problems. These two ideas are independent of each other and can therefore be used either separately or together. We consider all possibilities. For the first approach, we note that the zero vector can be taken as the initial basic (infeasible) solution for the linear programming problem and therefore, if the true signal is very sparse, some variants of the simplex method can be expected to take only a small number of pivots to arrive at a solution. We implemented one such variant and demonstrate a dramatic improvement in computation time on very sparse signals. The second approach requires a redesigned sensing mechanism in which the vector signal is stacked into a matrix. This allows us to exploit the Kronecker compressed sensing (KCS) mechanism. We show that the Kronecker sensing requires stronger conditions for perfect recovery compared to the original vector problem. However, the Kronecker sensing, modeled correctly, is a much sparser linear optimization problem. Hence, algorithms that benefit from sparse problem representation, such as interior-point methods, can solve the Kronecker

preprint2022arXiv

Neural graphical modelling in continuous-time: consistency guarantees and algorithms

The discovery of structure from time series data is a key problem in fields of study working with complex systems. Most identifiability results and learning algorithms assume the underlying dynamics to be discrete in time. Comparatively few, in contrast, explicitly define dependencies in infinitesimal intervals of time, independently of the scale of observation and of the regularity of sampling. In this paper, we consider score-based structure learning for the study of dynamical systems. We prove that for vector fields parameterized in a large class of neural networks, least squares optimization with adaptive regularization schemes consistently recovers directed graphs of local independencies in systems of stochastic differential equations. Using this insight, we propose a score-based learning algorithm based on penalized Neural Ordinary Differential Equations (modelling the mean process) that we show to be applicable to the general setting of irregularly-sampled multivariate time series and to outperform the state of the art across a range of dynamical systems.

preprint2021arXiv

Minimum Excess Risk in Bayesian Learning

We analyze the best achievable performance of Bayesian learning under generative models by defining and upper-bounding the minimum excess risk (MER): the gap between the minimum expected loss attainable by learning from data and the minimum expected loss that could be achieved if the model realization were known. The definition of MER provides a principled way to define different notions of uncertainties in Bayesian learning, including the aleatoric uncertainty and the minimum epistemic uncertainty. Two methods for deriving upper bounds for the MER are presented. The first method, generally suitable for Bayesian learning with a parametric generative model, upper-bounds the MER by the conditional mutual information between the model parameters and the quantity being predicted given the observed data. It allows us to quantify the rate at which the MER decays to zero as more data becomes available. Under realizable models, this method also relates the MER to the richness of the generative function class, notably the VC dimension in binary classification. The second method, particularly suitable for Bayesian learning with a parametric predictive model, relates the MER to the minimum estimation error of the model parameters from data. It explicitly shows how the uncertainty in model parameter estimation translates to the MER and to the final prediction uncertainty. We also extend the definition and analysis of MER to the setting with multiple model families and the setting with nonparametric models. Along the discussions we draw some comparisons between the MER in Bayesian learning and the excess risk in frequentist learning.

preprint2022arXiv

A Machine Learning Smartphone-based Sensing for Driver Behavior Classification

Driver behavior profiling is one of the main issues in the insurance industries and fleet management, thus being able to classify the driver behavior with low-cost mobile applications remains in the spotlight of autonomous driving. However, using mobile sensors may face the challenge of security, privacy, and trust issues. To overcome those challenges, we propose to collect data sensors using Carla Simulator available in smartphones (Accelerometer, Gyroscope, GPS) in order to classify the driver behavior using speed, acceleration, direction, the 3-axis rotation angles (Yaw, Pitch, Roll) taking into account the speed limit of the current road and weather conditions to better identify the risky behavior. Secondly, after fusing inter-axial data from multiple sensors into a single file, we explore different machine learning algorithms for time series classification to evaluate which algorithm results in the highest performance.

preprint2022arXiv

A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues from Digital Image Correlation Measurements

We present a data-driven workflow to biological tissue modeling, which aims to predict the displacement field based on digital image correlation (DIC) measurements under unseen loading scenarios, without postulating a specific constitutive model form nor possessing knowledges on the material microstructure. To this end, a material database is constructed from the DIC displacement tracking measurements of multiple biaxial stretching protocols on a porcine tricuspid valve anterior leaflet, with which we build a neural operator learning model. The material response is modeled as a solution operator from the loading to the resultant displacement field, with the material microstructure properties learned implicitly from the data and naturally embedded in the network parameters. Using various combinations of loading protocols, we compare the predictivity of this framework with finite element analysis based on the phenomenological Fung-type model. From in-distribution tests, the predictivity of our approach presents good generalizability to different loading conditions and outperforms the conventional constitutive modeling at approximately one order of magnitude. When tested on out-of-distribution loading ratios, the neural operator learning approach becomes less effective. To improve the generalizability of our framework, we propose a physics-guided neural operator learning model via imposing partial physics knowledge. This method is shown to improve the model's extrapolative performance in the small-deformation regime. Our results demonstrate that with sufficient data coverage and/or guidance from partial physics constraints, the data-driven approach can be a more effective method for modeling biological materials than the traditional constitutive modeling.

preprint2022arXiv

NeuRegenerate: A Framework for Visualizing Neurodegeneration

Recent advances in high-resolution microscopy have allowed scientists to better understand the underlying brain connectivity. However, due to the limitation that biological specimens can only be imaged at a single timepoint, studying changes to neural projections is limited to general observations using population analysis. In this paper, we introduce NeuRegenerate, a novel end-to-end framework for the prediction and visualization of changes in neural fiber morphology within a subject, for specified age-timepoints.To predict projections, we present neuReGANerator, a deep-learning network based on cycle-consistent generative adversarial network (cycleGAN) that translates features of neuronal structures in a region, across age-timepoints, for large brain microscopy volumes. We improve the reconstruction quality of neuronal structures by implementing a density multiplier and a new loss function, called the hallucination loss.Moreover, to alleviate artifacts that occur due to tiling of large input volumes, we introduce a spatial-consistency module in the training pipeline of neuReGANerator. We show that neuReGANerator has a reconstruction accuracy of 94% in predicting neuronal structures. Finally, to visualize the predicted change in projections, NeuRegenerate offers two modes: (1) neuroCompare to simultaneously visualize the difference in the structures of the neuronal projections, across the age timepoints, and (2) neuroMorph, a vesselness-based morphing technique to interactively visualize the transformation of the structures from one age-timepoint to the other. Our framework is designed specifically for volumes acquired using wide-field microscopy. We demonstrate our framework by visualizing the structural changes in neuronal fibers within the cholinergic system of the mouse brain between a young and old specimen.

preprint2020arXiv

A Data and Compute Efficient Design for Limited-Resources Deep Learning

Thanks to their improved data efficiency, equivariant neural networks have gained increased interest in the deep learning community. They have been successfully applied in the medical domain where symmetries in the data can be effectively exploited to build more accurate and robust models. To be able to reach a much larger body of patients, mobile, on-device implementations of deep learning solutions have been developed for medical applications. However, equivariant models are commonly implemented using large and computationally expensive architectures, not suitable to run on mobile devices. In this work, we design and test an equivariant version of MobileNetV2 and further optimize it with model quantization to enable more efficient inference. We achieve close-to state of the art performance on the Patch Camelyon (PCam) medical dataset while being more computationally efficient.

preprint2022arXiv

Approximate Network Motif Mining Via Graph Learning

Frequent and structurally related subgraphs, also known as network motifs, are valuable features of many graph datasets. However, the high computational complexity of identifying motif sets in arbitrary datasets (motif mining) has limited their use in many real-world datasets. By automatically leveraging statistical properties of datasets, machine learning approaches have shown promise in several tasks with combinatorial complexity and are therefore a promising candidate for network motif mining. In this work we seek to facilitate the development of machine learning approaches aimed at motif mining. We propose a formulation of the motif mining problem as a node labelling task. In addition, we build benchmark datasets and evaluation metrics which test the ability of models to capture different aspects of motif discovery such as motif number, size, topology, and scarcity. Next, we propose MotiFiesta, a first attempt at solving this problem in a fully differentiable manner with promising results on challenging baselines. Finally, we demonstrate through MotiFiesta that this learning setting can be applied simultaneously to general-purpose data mining and interpretable feature extraction for graph classification tasks.

preprint2022arXiv

ALBU: An approximate Loopy Belief message passing algorithm for LDA to improve performance on small data sets

Variational Bayes (VB) applied to latent Dirichlet allocation (LDA) has become the most popular algorithm for aspect modeling. While sufficiently successful in text topic extraction from large corpora, VB is less successful in identifying aspects in the presence of limited data. We present a novel variational message passing algorithm as applied to Latent Dirichlet Allocation (LDA) and compare it with the gold standard VB and collapsed Gibbs sampling. In situations where marginalisation leads to non-conjugate messages, we use ideas from sampling to derive approximate update equations. In cases where conjugacy holds, Loopy Belief update (LBU) (also known as Lauritzen-Spiegelhalter) is used. Our algorithm, ALBU (approximate LBU), has strong similarities with Variational Message Passing (VMP) (which is the message passing variant of VB). To compare the performance of the algorithms in the presence of limited data, we use data sets consisting of tweets and news groups. Additionally, to perform more fine grained evaluations and comparisons, we use simulations that enable comparisons with the ground truth via Kullback-Leibler divergence (KLD). Using coherence measures for the text corpora and KLD with the simulations we show that ALBU learns latent distributions more accurately than does VB, especially for smaller data sets.

preprint2022arXiv

Distilling Robust and Non-Robust Features in Adversarial Examples by Information Bottleneck

Adversarial examples, generated by carefully crafted perturbation, have attracted considerable attention in research fields. Recent works have argued that the existence of the robust and non-robust features is a primary cause of the adversarial examples, and investigated their internal interactions in the feature space. In this paper, we propose a way of explicitly distilling feature representation into the robust and non-robust features, using Information Bottleneck. Specifically, we inject noise variation to each feature unit and evaluate the information flow in the feature representation to dichotomize feature units either robust or non-robust, based on the noise variation magnitude. Through comprehensive experiments, we demonstrate that the distilled features are highly correlated with adversarial prediction, and they have human-perceptible semantic information by themselves. Furthermore, we present an attack mechanism intensifying the gradient of non-robust features that is directly related to the model prediction, and validate its effectiveness of breaking model robustness.

preprint2014arXiv

Mixed-norm Regularization for Brain Decoding

This work investigates the use of mixed-norm regularization for sensor selection in Event-Related Potential (ERP) based Brain-Computer Interfaces (BCI). The classification problem is cast as a discriminative optimization framework where sensor selection is induced through the use of mixed-norms. This framework is extended to the multi-task learning situation where several similar classification tasks related to different subjects are learned simultaneously. In this case, multi-task learning helps in leveraging data scarcity issue yielding to more robust classifiers. For this purpose, we have introduced a regularizer that induces both sensor selection and classifier similarities. The different regularization approaches are compared on three ERP datasets showing the interest of mixed-norm regularization in terms of sensor selection. The multi-task approaches are evaluated when a small number of learning examples are available yielding to significant performance improvements especially for subjects performing poorly.

preprint2022arXiv

Deep Partial Updating: Towards Communication Efficient Updating for On-device Inference

Emerging edge intelligence applications require the server to retrain and update deep neural networks deployed on remote edge nodes to leverage newly collected data samples. Unfortunately, it may be impossible in practice to continuously send fully updated weights to these edge nodes due to the highly constrained communication resource. In this paper, we propose the weight-wise deep partial updating paradigm, which smartly selects a small subset of weights to update in each server-to-edge communication round, while achieving a similar performance compared to full updating. Our method is established through analytically upper-bounding the loss difference between partial updating and full updating, and only updates the weights which make the largest contributions to the upper bound. Extensive experimental results demonstrate the efficacy of our partial updating methodology which achieves a high inference accuracy while updating a rather small number of weights.

preprint2019arXiv

Learning Representations for Neural Network-Based Classification Using the Information Bottleneck Principle

In this theory paper, we investigate training deep neural networks (DNNs) for classification via minimizing the information bottleneck (IB) functional. We show that the resulting optimization problem suffers from two severe issues: First, for deterministic DNNs, either the IB functional is infinite for almost all values of network parameters, making the optimization problem ill-posed, or it is piecewise constant, hence not admitting gradient-based optimization methods. Second, the invariance of the IB functional under bijections prevents it from capturing properties of the learned representation that are desirable for classification, such as robustness and simplicity. We argue that these issues are partly resolved for stochastic DNNs, DNNs that include a (hard or soft) decision rule, or by replacing the IB functional with related, but more well-behaved cost functions. We conclude that recent successes reported about training DNNs using the IB framework must be attributed to such solutions. As a side effect, our results indicate limitations of the IB framework for the analysis of DNNs. We also note that rather than trying to repair the inherent problems in the IB functional, a bette

preprint2020arXiv

Tree-Projected Gradient Descent for Estimating Gradient-Sparse Parameters on Graphs

We study estimation of a gradient-sparse parameter vector $\boldsymbolθ^* \in \mathbb{R}^p$, having strong gradient-sparsity $s^*:=\|\nabla_G \boldsymbolθ^*\|_0$ on an underlying graph $G$. Given observations $Z_1,\ldots,Z_n$ and a smooth, convex loss function $\mathcal{L}$ for which $\boldsymbolθ^*$ minimizes the population risk $\mathbb{E}[\mathcal{L}(\boldsymbolθ;Z_1,\ldots,Z_n)]$, we propose to estimate $\boldsymbolθ^*$ by a projected gradient descent algorithm that iteratively and approximately projects gradient steps onto spaces of vectors having small gradient-sparsity over low-degree spanning trees of $G$. We show that, under suitable restricted strong convexity and smoothness assumptions for the loss, the resulting estimator achieves the squared-error risk $\frac{s^*}{n} \log (1+\frac{p}{s^*})$ up to a multiplicative constant that is independent of $G$. In contrast, previous polynomial-time algorithms have only been shown to achieve this guarantee in more specialized settings, or under additional assumptions for $G$ and/or the sparsity pattern of $\nabla_G \boldsymbolθ^*$. As applications of our general framework, we apply our results to the examples of linear models and g

preprint2026arXiv

Evaluating Memory Condensation Strategies for Coding Agents in Data-Driven Scientific Discovery

Coding agents accumulate extensive context during long-running tasks, yet fixed context windows force practitioners to choose between truncation and task failure. While numerous memory condensation strategies have been proposed, from simple sliding windows to LLM-generated summaries, no systematic comparison exists to guide strategy selection, especially in scientific discovery tasks. We evaluate eight memory condensation strategies using GPT-4o on sixty DiscoveryBench tasks spanning six scientific domains (480 total evaluations). We find that no condenser significantly alters hypothesis quality, while LLM-based condensers increase token costs by 24-94 percent, and masking tool-call outputs achieves an 8.6 percent net savings. We also observe that the optimal condenser for data-driven scientific discovery varies by scientific domain and task length.

preprint2022arXiv

Optimizing Data Collection in Deep Reinforcement Learning

Reinforcement learning (RL) workloads take a notoriously long time to train due to the large number of samples collected at run-time from simulators. Unfortunately, cluster scale-up approaches remain expensive, and commonly used CPU implementations of simulators induce high overhead when switching back and forth between GPU computations. We explore two optimizations that increase RL data collection efficiency by increasing GPU utilization: (1) GPU vectorization: parallelizing simulation on the GPU for increased hardware parallelism, and (2) simulator kernel fusion: fusing multiple simulation steps to run in a single GPU kernel launch to reduce global memory bandwidth requirements. We find that GPU vectorization can achieve up to $1024\times$ speedup over commonly used CPU simulators. We profile the performance of different implementations and show that for a simple simulator, ML compiler implementations (XLA) of GPU vectorization outperform a DNN framework (PyTorch) by $13.4\times$ by reducing CPU overhead from repeated Python to DL backend API calls. We show that simulator kernel fusion speedups with a simple simulator are $11.3\times$ and increase by up to $1024\times$ as simulator complexity increases in terms of memory bandwidth requirements. We show that the speedups from simulator kernel fusion are orthogonal and combinable with GPU vectorization, leading to a multiplicative speedup.

preprint2015arXiv

Unbiased Bayes for Big Data: Paths of Partial Posteriors

A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn from an approximate posterior. However, its feasibility is being challenged in the era of so called Big Data as all data needs to be processed in every iteration. Realising that such simulation is an unnecessarily hard problem if the goal is estimation, we construct a computationally scalable methodology that allows unbiased estimation of the required expectations -- without explicit simulation from the full posterior. The scheme's variance is finite by construction and straightforward to control, leading to algorithms that are provably unbiased and naturally arrive at a desired error tolerance. This is achieved at an average computational complexity that is sub-linear in the size of the dataset and its free parameters are easy to tune. We demonstrate the utility and generality of the methodology on a range of common statistical models applied to large-scale benchmark and real-world datasets.

preprint2012arXiv

Sparse Trace Norm Regularization

We study the problem of estimating multiple predictive functions from a dictionary of basis functions in the nonparametric regression setting. Our estimation scheme assumes that each predictive function can be estimated in the form of a linear combination of the basis functions. By assuming that the coefficient matrix admits a sparse low-rank structure, we formulate the function estimation problem as a convex program regularized by the trace norm and the $\ell_1$-norm simultaneously. We propose to solve the convex program using the accelerated gradient (AG) method and the alternating direction method of multipliers (ADMM) respectively; we also develop efficient algorithms to solve the key components in both AG and ADMM. In addition, we conduct theoretical analysis on the proposed function estimation scheme: we derive a key property of the optimal solution to the convex program; based on an assumption on the basis functions, we establish a performance bound of the proposed function estimation scheme (via the composite regularization). Simulation studies demonstrate the effectiveness and efficiency of the proposed algorithms.

preprint2026arXiv

Bootstrap Off-policy with World Model

Online planning has proven effective in reinforcement learning (RL) for improving sample efficiency and final performance. However, using planning for environment interaction inevitably introduces a divergence between the collected data and the policy's actual behaviors, degrading both model learning and policy improvement. To address this, we propose BOOM (Bootstrap Off-policy with WOrld Model), a framework that tightly integrates planning and off-policy learning through a bootstrap loop: the policy initializes the planner, and the planner refines actions to bootstrap the policy through behavior alignment. This loop is supported by a jointly learned world model, which enables the planner to simulate future trajectories and provides value targets to facilitate policy improvement. The core of BOOM is a likelihood-free alignment loss that bootstraps the policy using the planner's non-parametric action distribution, combined with a soft value-weighted mechanism that prioritizes high-return behaviors and mitigates variability in the planner's action quality within the replay buffer. Experiments on the high-dimensional DeepMind Control Suite and Humanoid-Bench show that BOOM