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Weiran Wang

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

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Machine LearningComputation and Languageeess.ASSoundmath.OCComputer VisionMethodologyNeural and Evolutionary ComputingArtificial Intelligenceeess.IV

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Published work

33 published item(s)

preprint2026arXiv

Penalty-Based First-Order Methods for Bilevel Optimization with Minimax and Constrained Lower-Level Problems

We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel optimization and minimax optimization separately, existing methods mainly focus on bilevel optimization with lower-level minimization problems, often under strong convexity assumptions, and are not directly applicable to the minimax lower-level setting considered here. To address this gap, we develop penalty-based first-order methods for bilevel minimax optimization without requiring strong convexity of the lower-level problem. In the deterministic setting, we establish that the proposed method finds an $ε$-KKT point with $\tilde{O}(ε^{-4})$ oracle complexity. We further show that bilevel problems with convex constrained lower-level minimization can be reformulated as special cases of our framework via Lagrangian duality, leading to an $\tilde{O}(ε^{-4})$ complexity bound that improves upon the existing $\tilde{O}(ε^{-7})$ result. Finally, we extend our approach to the stochastic setting, where only stochastic gradient oracles are available, and prove that the proposed stochastic method finds a nearly $ε$-KKT point with $\tilde{O}(ε^{-9})$ oracle complexity.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Unified Cascaded Encoder ASR Model for Dynamic Model Sizes

In this paper, we propose a dynamic cascaded encoder Automatic Speech Recognition (ASR) model, which unifies models for different deployment scenarios. Moreover, the model can significantly reduce model size and power consumption without loss of quality. Namely, with the dynamic cascaded encoder model, we explore three techniques to maximally boost the performance of each model size: 1) Use separate decoders for each sub-model while sharing the encoders; 2) Use funnel-pooling to improve the encoder efficiency; 3) Balance the size of causal and non-causal encoders to improve quality and fit deployment constraints. Overall, the proposed large-medium model has 30% smaller size and reduces power consumption by 33%, compared to the baseline cascaded encoder model. The triple-size model that unifies the large, medium, and small models achieves 37% total size reduction with minimal quality loss, while substantially reducing the engineering efforts of having separate models.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Improving Deliberation by Text-Only and Semi-Supervised Training

Text-only and semi-supervised training based on audio-only data has gained popularity recently due to the wide availability of unlabeled text and speech data. In this work, we propose incorporating text-only and semi-supervised training into an attention-based deliberation model. By incorporating text-only data in training a bidirectional encoder representation from transformer (BERT) for the deliberation text encoder, and large-scale text-to-speech and audio-only utterances using joint acoustic and text decoder (JATD) and semi-supervised training, we achieved 4%-12% WER reduction for various tasks compared to the baseline deliberation. Compared to a state-of-the-art language model (LM) rescoring method, the deliberation model reduces the Google Voice Search WER by 11% relative. We show that the deliberation model also achieves a positive human side-by-side evaluation compared to the state-of-the-art LM rescorer with reasonable endpointer latencies.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Improving Rare Word Recognition with LM-aware MWER Training

Language models (LMs) significantly improve the recognition accuracy of end-to-end (E2E) models on words rarely seen during training, when used in either the shallow fusion or the rescoring setups. In this work, we introduce LMs in the learning of hybrid autoregressive transducer (HAT) models in the discriminative training framework, to mitigate the training versus inference gap regarding the use of LMs. For the shallow fusion setup, we use LMs during both hypotheses generation and loss computation, and the LM-aware MWER-trained model achieves 10\% relative improvement over the model trained with standard MWER on voice search test sets containing rare words. For the rescoring setup, we learn a small neural module to generate per-token fusion weights in a data-dependent manner. This model achieves the same rescoring WER as regular MWER-trained model, but without the need for sweeping fusion weights.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

NTIRE 2022 Challenge on Efficient Super-Resolution: Methods and Results

This paper reviews the NTIRE 2022 challenge on efficient single image super-resolution with focus on the proposed solutions and results. The task of the challenge was to super-resolve an input image with a magnification factor of $\times$4 based on pairs of low and corresponding high resolution images. The aim was to design a network for single image super-resolution that achieved improvement of efficiency measured according to several metrics including runtime, parameters, FLOPs, activations, and memory consumption while at least maintaining the PSNR of 29.00dB on DIV2K validation set. IMDN is set as the baseline for efficiency measurement. The challenge had 3 tracks including the main track (runtime), sub-track one (model complexity), and sub-track two (overall performance). In the main track, the practical runtime performance of the submissions was evaluated. The rank of the teams were determined directly by the absolute value of the average runtime on the validation set and test set. In sub-track one, the number of parameters and FLOPs were considered. And the individual rankings of the two metrics were summed up to determine a final ranking in this track. In sub-track two, all of the five metrics mentioned in the description of the challenge including runtime, parameter count, FLOPs, activations, and memory consumption were considered. Similar to sub-track one, the rankings of five metrics were summed up to determine a final ranking. The challenge had 303 registered participants, and 43 teams made valid submissions. They gauge the state-of-the-art in efficient single image super-resolution.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Streaming Align-Refine for Non-autoregressive Deliberation

We propose a streaming non-autoregressive (non-AR) decoding algorithm to deliberate the hypothesis alignment of a streaming RNN-T model. Our algorithm facilitates a simple greedy decoding procedure, and at the same time is capable of producing the decoding result at each frame with limited right context, thus enjoying both high efficiency and low latency. These advantages are achieved by converting the offline Align-Refine algorithm to be streaming-compatible, with a novel transformer decoder architecture that performs local self-attentions for both text and audio, and a time-aligned cross-attention at each layer. Furthermore, we perform discriminative training of our model with the minimum word error rate (MWER) criterion, which has not been done in the non-AR decoding literature. Experiments on voice search datasets and Librispeech show that with reasonable right context, our streaming model performs as well as the offline counterpart, and discriminative training leads to further WER gain when the first-pass model has small capacity.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspective

Multiple views of data, both naturally acquired (e.g., image and audio) and artificially produced (e.g., via adding different noise to data samples), have proven useful in enhancing representation learning. Natural views are often handled by multiview analysis tools, e.g., (deep) canonical correlation analysis [(D)CCA], while the artificial ones are frequently used in self-supervised learning (SSL) paradigms, e.g., BYOL and Barlow Twins. Both types of approaches often involve learning neural feature extractors such that the embeddings of data exhibit high cross-view correlations. Although intuitive, the effectiveness of correlation-based neural embedding is mostly empirically validated. This work aims to understand latent correlation maximization-based deep multiview learning from a latent component identification viewpoint. An intuitive generative model of multiview data is adopted, where the views are different nonlinear mixtures of shared and private components. Since the shared components are view/distortion-invariant, representing the data using such components is believed to reveal the identity of the samples effectively and robustly. Under this model, latent correlation maximization is shown to guarantee the extraction of the shared components across views (up to certain ambiguities). In addition, it is further shown that the private information in each view can be provably disentangled from the shared using proper regularization design. A finite sample analysis, which has been rare in nonlinear mixture identifiability study, is also presented. The theoretical results and newly designed regularization are tested on a series of tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Representation Learning for Sequence Data with Deep Autoencoding Predictive Components

We propose Deep Autoencoding Predictive Components (DAPC) -- a self-supervised representation learning method for sequence data, based on the intuition that useful representations of sequence data should exhibit a simple structure in the latent space. We encourage this latent structure by maximizing an estimate of predictive information of latent feature sequences, which is the mutual information between past and future windows at each time step. In contrast to the mutual information lower bound commonly used by contrastive learning, the estimate of predictive information we adopt is exact under a Gaussian assumption. Additionally, it can be computed without negative sampling. To reduce the degeneracy of the latent space extracted by powerful encoders and keep useful information from the inputs, we regularize predictive information learning with a challenging masked reconstruction loss. We demonstrate that our method recovers the latent space of noisy dynamical systems, extracts predictive features for forecasting tasks, and improves automatic speech recognition when used to pretrain the encoder on large amounts of unlabeled data.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A Comparison of Pooling Methods on LSTM Models for Rare Acoustic Event Classification

Acoustic event classification (AEC) and acoustic event detection (AED) refer to the task of detecting whether specific target events occur in audios. As long short-term memory (LSTM) leads to state-of-the-art results in various speech related tasks, it is employed as a popular solution for AEC as well. This paper focuses on investigating the dynamics of LSTM model on AEC tasks. It includes a detailed analysis on LSTM memory retaining, and a benchmarking of nine different pooling methods on LSTM models using 1.7M generated mixture clips of multiple events with different signal-to-noise ratios. This paper focuses on understanding: 1) utterance-level classification accuracy; 2) sensitivity to event position within an utterance. The analysis is done on the dataset for the detection of rare sound events from DCASE 2017 Challenge. We find max pooling on the prediction level to perform the best among the nine pooling approaches in terms of classification accuracy and insensitivity to event position within an utterance. To authors' best knowledge, this is the first kind of such work focused on LSTM dynamics for AEC tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Data Techniques For Online End-to-end Speech Recognition

Practitioners often need to build ASR systems for new use cases in a short amount of time, given limited in-domain data. While recently developed end-to-end methods largely simplify the modeling pipelines, they still suffer from the data sparsity issue. In this work, we explore a few simple-to-implement techniques for building online ASR systems in an end-to-end fashion, with a small amount of transcribed data in the target domain. These techniques include data augmentation in the target domain, domain adaptation using models previously trained on a large source domain, and knowledge distillation on non-transcribed target domain data, using an adapted bi-directional model as the teacher; they are applicable in real scenarios with different types of resources. Our experiments demonstrate that each technique is independently useful in the improvement of the online ASR performance in the target domain.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Semi-supervised ASR by End-to-end Self-training

While deep learning based end-to-end automatic speech recognition (ASR) systems have greatly simplified modeling pipelines, they suffer from the data sparsity issue. In this work, we propose a self-training method with an end-to-end system for semi-supervised ASR. Starting from a Connectionist Temporal Classification (CTC) system trained on the supervised data, we iteratively generate pseudo-labels on a mini-batch of unsupervised utterances with the current model, and use the pseudo-labels to augment the supervised data for immediate model update. Our method retains the simplicity of end-to-end ASR systems, and can be seen as performing alternating optimization over a well-defined learning objective. We also perform empirical investigations of our method, regarding the effect of data augmentation, decoding beamsize for pseudo-label generation, and freshness of pseudo-labels. On a commonly used semi-supervised ASR setting with the WSJ corpus, our method gives 14.4% relative WER improvement over a carefully-trained base system with data augmentation, reducing the performance gap between the base system and the oracle system by 50%.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Unsupervised Pre-training of Bidirectional Speech Encoders via Masked Reconstruction

We propose an approach for pre-training speech representations via a masked reconstruction loss. Our pre-trained encoder networks are bidirectional and can therefore be used directly in typical bidirectional speech recognition models. The pre-trained networks can then be fine-tuned on a smaller amount of supervised data for speech recognition. Experiments with this approach on the LibriSpeech and Wall Street Journal corpora show promising results. We find that the main factors that lead to speech recognition improvements are: masking segments of sufficient width in both time and frequency, pre-training on a much larger amount of unlabeled data than the labeled data, and domain adaptation when the unlabeled and labeled data come from different domains. The gain from pre-training is additive to that of supervised data augmentation.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Deep convolutional acoustic word embeddings using word-pair side information

Recent studies have been revisiting whole words as the basic modelling unit in speech recognition and query applications, instead of phonetic units. Such whole-word segmental systems rely on a function that maps a variable-length speech segment to a vector in a fixed-dimensional space; the resulting acoustic word embeddings need to allow for accurate discrimination between different word types, directly in the embedding space. We compare several old and new approaches in a word discrimination task. Our best approach uses side information in the form of known word pairs to train a Siamese convolutional neural network (CNN): a pair of tied networks that take two speech segments as input and produce their embeddings, trained with a hinge loss that separates same-word pairs and different-word pairs by some margin. A word classifier CNN performs similarly, but requires much stronger supervision. Both types of CNNs yield large improvements over the best previously published results on the word discrimination task.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Discriminative Segmental Cascades for Feature-Rich Phone Recognition

Discriminative segmental models, such as segmental conditional random fields (SCRFs) and segmental structured support vector machines (SSVMs), have had success in speech recognition via both lattice rescoring and first-pass decoding. However, such models suffer from slow decoding, hampering the use of computationally expensive features, such as segment neural networks or other high-order features. A typical solution is to use approximate decoding, either by beam pruning in a single pass or by beam pruning to generate a lattice followed by a second pass. In this work, we study discriminative segmental models trained with a hinge loss (i.e., segmental structured SVMs). We show that beam search is not suitable for learning rescoring models in this approach, though it gives good approximate decoding performance when the model is already well-trained. Instead, we consider an approach inspired by structured prediction cascades, which use max-marginal pruning to generate lattices. We obtain a high-accuracy phonetic recognition system with several expensive feature types: a segment neural network, a second-order language model, and second-order phone boundary features.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Efficient Globally Convergent Stochastic Optimization for Canonical Correlation Analysis

We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently proposed to solve this problem, no global convergence guarantee was provided by any of them. Inspired by the alternating least squares/power iterations formulation of CCA, and the shift-and-invert preconditioning method for PCA, we propose two globally convergent meta-algorithms for CCA, both of which transform the original problem into sequences of least squares problems that need only be solved approximately. We instantiate the meta-algorithms with state-of-the-art SGD methods and obtain time complexities that significantly improve upon that of previous work. Experimental results demonstrate their superior performance.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Efficient Segmental Cascades for Speech Recognition

Discriminative segmental models offer a way to incorporate flexible feature functions into speech recognition. However, their appeal has been limited by their computational requirements, due to the large number of possible segments to consider. Multi-pass cascades of segmental models introduce features of increasing complexity in different passes, where in each pass a segmental model rescores lattices produced by a previous (simpler) segmental model. In this paper, we explore several ways of making segmental cascades efficient and practical: reducing the feature set in the first pass, frame subsampling, and various pruning approaches. In experiments on phonetic recognition, we find that with a combination of such techniques, it is possible to maintain competitive performance while greatly reducing decoding, pruning, and training time.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

End-to-End Training Approaches for Discriminative Segmental Models

Recent work on discriminative segmental models has shown that they can achieve competitive speech recognition performance, using features based on deep neural frame classifiers. However, segmental models can be more challenging to train than standard frame-based approaches. While some segmental models have been successfully trained end to end, there is a lack of understanding of their training under different settings and with different losses. We investigate a model class based on recent successful approaches, consisting of a linear model that combines segmental features based on an LSTM frame classifier. Similarly to hybrid HMM-neural network models, segmental models of this class can be trained in two stages (frame classifier training followed by linear segmental model weight training), end to end (joint training of both frame classifier and linear weights), or with end-to-end fine-tuning after two-stage training. We study segmental models trained end to end with hinge loss, log loss, latent hinge loss, and marginal log loss. We consider several losses for the case where training alignments are available as well as where they are not. We find that in general, marginal log loss provides the most consistent strong performance without requiring ground-truth alignments. We also find that training with dropout is very important in obtaining good performance with end-to-end training. Finally, the best results are typically obtained by a combination of two-stage training and fine-tuning.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Large-Scale Approximate Kernel Canonical Correlation Analysis

Kernel canonical correlation analysis (KCCA) is a nonlinear multi-view representation learning technique with broad applicability in statistics and machine learning. Although there is a closed-form solution for the KCCA objective, it involves solving an $N\times N$ eigenvalue system where $N$ is the training set size, making its computational requirements in both memory and time prohibitive for large-scale problems. Various approximation techniques have been developed for KCCA. A commonly used approach is to first transform the original inputs to an $M$-dimensional random feature space so that inner products in the feature space approximate kernel evaluations, and then apply linear CCA to the transformed inputs. In many applications, however, the dimensionality $M$ of the random feature space may need to be very large in order to obtain a sufficiently good approximation; it then becomes challenging to perform the linear CCA step on the resulting very high-dimensional data matrices. We show how to use a stochastic optimization algorithm, recently proposed for linear CCA and its neural-network extension, to further alleviate the computation requirements of approximate KCCA. This approach allows us to run approximate KCCA on a speech dataset with $1.4$ million training samples and a random feature space of dimensionality $M=100000$ on a typical workstation.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Lexicon-Free Fingerspelling Recognition from Video: Data, Models, and Signer Adaptation

We study the problem of recognizing video sequences of fingerspelled letters in American Sign Language (ASL). Fingerspelling comprises a significant but relatively understudied part of ASL. Recognizing fingerspelling is challenging for a number of reasons: It involves quick, small motions that are often highly coarticulated; it exhibits significant variation between signers; and there has been a dearth of continuous fingerspelling data collected. In this work we collect and annotate a new data set of continuous fingerspelling videos, compare several types of recognizers, and explore the problem of signer variation. Our best-performing models are segmental (semi-Markov) conditional random fields using deep neural network-based features. In the signer-dependent setting, our recognizers achieve up to about 92% letter accuracy. The multi-signer setting is much more challenging, but with neural network adaptation we achieve up to 83% letter accuracies in this setting.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Network Inference by Learned Node-Specific Degree Prior

We propose a novel method for network inference from partially observed edges using a node-specific degree prior. The degree prior is derived from observed edges in the network to be inferred, and its hyper-parameters are determined by cross validation. Then we formulate network inference as a matrix completion problem regularized by our degree prior. Our theoretical analysis indicates that this prior favors a network following the learned degree distribution, and may lead to improved network recovery error bound than previous work. Experimental results on both simulated and real biological networks demonstrate the superior performance of our method in various settings.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Nonparametric Canonical Correlation Analysis

Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep neural network methods. These approaches seek maximally correlated projections among families of functions, which the user specifies (by choosing a kernel or neural network structure), and are computationally demanding. Interestingly, the theory of nonlinear CCA, without functional restrictions, had been studied in the population setting by Lancaster already in the 1950s, but these results have not inspired practical algorithms. We revisit Lancaster's theory to devise a practical algorithm for nonparametric CCA (NCCA). Specifically, we show that the solution can be expressed in terms of the singular value decomposition of a certain operator associated with the joint density of the views. Thus, by estimating the population density from data, NCCA reduces to solving an eigenvalue system, superficially like kernel CCA but, importantly, without requiring the inversion of any kernel matrix. We also derive a partially linear CCA (PLCCA) variant in which one of the views undergoes a linear projection while the other is nonparametric. Using a kernel density estimate based on a small number of nearest neighbors, our NCCA and PLCCA algorithms are memory-efficient, often run much faster, and perform better than kernel CCA and comparable to deep CCA.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

On Column Selection in Approximate Kernel Canonical Correlation Analysis

We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nyström approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the training set. When building low-rank kernel approximations in KCCA, previous work mostly samples the landmarks uniformly at random from the training set. We propose novel strategies for sampling the landmarks non-uniformly based on a version of statistical leverage scores recently developed for kernel ridge regression. We study the approximation accuracy of the proposed non-uniform sampling strategy, develop an incremental algorithm that explores the path of approximation ranks and facilitates efficient model selection, and derive the kernel stability of out-of-sample mapping for our method. Experimental results on both synthetic and real-world datasets demonstrate the promise of our method.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

On Deep Multi-View Representation Learning: Objectives and Optimization

We consider learning representations (features) in the setting in which we have access to multiple unlabeled views of the data for learning while only one view is available for downstream tasks. Previous work on this problem has proposed several techniques based on deep neural networks, typically involving either autoencoder-like networks with a reconstruction objective or paired feedforward networks with a batch-style correlation-based objective. We analyze several techniques based on prior work, as well as new variants, and compare them empirically on image, speech, and text tasks. We find an advantage for correlation-based representation learning, while the best results on most tasks are obtained with our new variant, deep canonically correlated autoencoders (DCCAE). We also explore a stochastic optimization procedure for minibatch correlation-based objectives and discuss the time/performance trade-offs for kernel-based and neural network-based implementations.

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preprint2016arXiv

Signer-independent Fingerspelling Recognition with Deep Neural Network Adaptation

We study the problem of recognition of fingerspelled letter sequences in American Sign Language in a signer-independent setting. Fingerspelled sequences are both challenging and important to recognize, as they are used for many content words such as proper nouns and technical terms. Previous work has shown that it is possible to achieve almost 90% accuracies on fingerspelling recognition in a signer-dependent setting. However, the more realistic signer-independent setting presents challenges due to significant variations among signers, coupled with the dearth of available training data. We investigate this problem with approaches inspired by automatic speech recognition. We start with the best-performing approaches from prior work, based on tandem models and segmental conditional random fields (SCRFs), with features based on deep neural network (DNN) classifiers of letters and phonological features. Using DNN adaptation, we find that it is possible to bridge a large part of the gap between signer-dependent and signer-independent performance. Using only about 115 transcribed words for adaptation from the target signer, we obtain letter accuracies of up to 82.7% with frame-level adaptation labels and 69.7% with only word labels.

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preprint2015arXiv

Stochastic Optimization for Deep CCA via Nonlinear Orthogonal Iterations

Deep CCA is a recently proposed deep neural network extension to the traditional canonical correlation analysis (CCA), and has been successful for multi-view representation learning in several domains. However, stochastic optimization of the deep CCA objective is not straightforward, because it does not decouple over training examples. Previous optimizers for deep CCA are either batch-based algorithms or stochastic optimization using large minibatches, which can have high memory consumption. In this paper, we tackle the problem of stochastic optimization for deep CCA with small minibatches, based on an iterative solution to the CCA objective, and show that we can achieve as good performance as previous optimizers and thus alleviate the memory requirement.

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preprint2014arXiv

LASS: a simple assignment model with Laplacian smoothing

We consider the problem of learning soft assignments of $N$ items to $K$ categories given two sources of information: an item-category similarity matrix, which encourages items to be assigned to categories they are similar to (and to not be assigned to categories they are dissimilar to), and an item-item similarity matrix, which encourages similar items to have similar assignments. We propose a simple quadratic programming model that captures this intuition. We give necessary conditions for its solution to be unique, define an out-of-sample mapping, and derive a simple, effective training algorithm based on the alternating direction method of multipliers. The model predicts reasonable assignments from even a few similarity values, and can be seen as a generalization of semisupervised learning. It is particularly useful when items naturally belong to multiple categories, as for example when annotating documents with keywords or pictures with tags, with partially tagged items, or when the categories have complex interrelations (e.g. hierarchical) that are unknown.

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preprint2014arXiv

The Laplacian K-modes algorithm for clustering

In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is challenging with data having a nonconvex or manifold structure, as with images or text. We introduce a new algorithm, Laplacian K-modes, which naturally combines three powerful ideas in clustering: the explicit use of assignment variables (as in K-means); the estimation of cluster centroids which are modes of each cluster's density estimate (as in mean-shift); and the regularizing effect of the graph Laplacian, which encourages similar assignments for nearby points (as in spectral clustering). The optimization algorithm alternates an assignment step, which is a convex quadratic program, and a mean-shift step, which separates for each cluster centroid. The algorithm finds meaningful density estimates for each cluster, even with challenging problems where the clusters have manifold structure, are highly nonconvex or in high dimension. It also provides centroids that are valid patterns, truly representative of their cluster (unlike K-means), and an out-of-sample mapping that predicts soft assignments for a new point.

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preprint2014arXiv

The role of dimensionality reduction in linear classification

Dimensionality reduction (DR) is often used as a preprocessing step in classification, but usually one first fixes the DR mapping, possibly using label information, and then learns a classifier (a filter approach). Best performance would be obtained by optimizing the classification error jointly over DR mapping and classifier (a wrapper approach), but this is a difficult nonconvex problem, particularly with nonlinear DR. Using the method of auxiliary coordinates, we give a simple, efficient algorithm to train a combination of nonlinear DR and a classifier, and apply it to a RBF mapping with a linear SVM. This alternates steps where we train the RBF mapping and a linear SVM as usual regression and classification, respectively, with a closed-form step that coordinates both. The resulting nonlinear low-dimensional classifier achieves classification errors competitive with the state-of-the-art but is fast at training and testing, and allows the user to trade off runtime for classification accuracy easily. We then study the role of nonlinear DR in linear classification, and the interplay between the DR mapping, the number of latent dimensions and the number of classes. When trained jointly, the DR mapping takes an extreme role in eliminating variation: it tends to collapse classes in latent space, erasing all manifold structure, and lay out class centroids so they are linearly separable with maximum margin.

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preprint2013arXiv

The K-modes algorithm for clustering

Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a K-modes objective function by combining the notions of density and cluster assignment. The algorithm becomes K-means and K-medoids in the limit of very large and very small scales. Computationally, it is slightly slower than K-means but much faster than mean-shift or K-medoids. Unlike K-means, it is able to find centroids that are valid patterns, truly representative of a cluster, even with nonconvex clusters, and appears robust to outliers and misspecification of the scale and number of clusters.

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preprint2012arXiv

Distributed optimization of deeply nested systems

In science and engineering, intelligent processing of complex signals such as images, sound or language is often performed by a parameterized hierarchy of nonlinear processing layers, sometimes biologically inspired. Hierarchical systems (or, more generally, nested systems) offer a way to generate complex mappings using simple stages. Each layer performs a different operation and achieves an ever more sophisticated representation of the input, as, for example, in an deep artificial neural network, an object recognition cascade in computer vision or a speech front-end processing. Joint estimation of the parameters of all the layers and selection of an optimal architecture is widely considered to be a difficult numerical nonconvex optimization problem, difficult to parallelize for execution in a distributed computation environment, and requiring significant human expert effort, which leads to suboptimal systems in practice. We describe a general mathematical strategy to learn the parameters and, to some extent, the architecture of nested systems, called the method of auxiliary coordinates (MAC). This replaces the original problem involving a deeply nested function with a constrained problem involving a different function in an augmented space without nesting. The constrained problem may be solved with penalty-based methods using alternating optimization over the parameters and the auxiliary coordinates. MAC has provable convergence, is easy to implement reusing existing algorithms for single layers, can be parallelized trivially and massively, applies even when parameter derivatives are not available or not desirable, and is competitive with state-of-the-art nonlinear optimizers even in the serial computation setting, often providing reasonable models within a few iterations.

0 citations0 reviewsNo code linkedOpen access