24 Papers

NADec 21, 2016
Online and stochastic Douglas-Rachford splitting method for large scale machine learning

Ziqiang Shi, Rujie Liu

Online and stochastic learning has emerged as powerful tool in large scale optimization. In this work, we generalize the Douglas-Rachford splitting (DRs) method for minimizing composite functions to online and stochastic settings (to our best knowledge this is the first time DRs been generalized to sequential version). We first establish an $O(1/\sqrt{T})$ regret bound for batch DRs method. Then we proved that the online DRs splitting method enjoy an $O(1)$ regret bound and stochastic DRs splitting has a convergence rate of $O(1/\sqrt{T})$. The proof is simple and intuitive, and the results and technique can be served as a initiate for the research on the large scale machine learning employ the DRs method. Numerical experiments of the proposed method demonstrate the effectiveness of the online and stochastic update rule, and further confirm our regret and convergence analysis.

CVAug 14, 2024
RTAT: A Robust Two-stage Association Tracker for Multi-Object Tracking

Song Guo, Rujie Liu, Narishige Abe

Data association is an essential part in the tracking-by-detection based Multi-Object Tracking (MOT). Most trackers focus on how to design a better data association strategy to improve the tracking performance. The rule-based handcrafted association methods are simple and highly efficient but lack generalization capability to deal with complex scenes. While the learnt association methods can learn high-order contextual information to deal with various complex scenes, but they have the limitations of higher complexity and cost. To address these limitations, we propose a Robust Two-stage Association Tracker, named RTAT. The first-stage association is performed between tracklets and detections to generate tracklets with high purity, and the second-stage association is performed between tracklets to form complete trajectories. For the first-stage association, we use a simple data association strategy to generate tracklets with high purity by setting a low threshold for the matching cost in the assignment process. We conduct the tracklet association in the second-stage based on the framework of message-passing GNN. Our method models the tracklet association as a series of edge classification problem in hierarchical graphs, which can recursively merge short tracklets into longer ones. Our tracker RTAT ranks first on the test set of MOT17 and MOT20 benchmarks in most of the main MOT metrics: HOTA, IDF1, and AssA. We achieve 67.2 HOTA, 84.7 IDF1, and 69.7 AssA on MOT17, and 66.2 HOTA, 82.5 IDF1, and 68.1 AssA on MOT20.

CVFeb 10
Scalpel: Fine-Grained Alignment of Attention Activation Manifolds via Mixture Gaussian Bridges to Mitigate Multimodal Hallucination

Ziqiang Shi, Rujie Liu, Shanshan Yu et al.

Rapid progress in large vision-language models (LVLMs) has achieved unprecedented performance in vision-language tasks. However, due to the strong prior of large language models (LLMs) and misaligned attention across modalities, LVLMs often generate outputs inconsistent with visual content - termed hallucination. To address this, we propose \textbf{Scalpel}, a method that reduces hallucination by refining attention activation distributions toward more credible regions. Scalpel predicts trusted attention directions for each head in Transformer layers during inference and adjusts activations accordingly. It employs a Gaussian mixture model to capture multi-peak distributions of attention in trust and hallucination manifolds, and uses entropic optimal transport (equivalent to Schrödinger bridge problem) to map Gaussian components precisely. During mitigation, Scalpel dynamically adjusts intervention strength and direction based on component membership and mapping relationships between hallucination and trust activations. Extensive experiments across multiple datasets and benchmarks demonstrate that Scalpel effectively mitigates hallucinations, outperforming previous methods and achieving state-of-the-art performance. Moreover, Scalpel is model- and data-agnostic, requiring no additional computation, only a single decoding step.

CVFeb 10
SchröMind: Mitigating Hallucinations in Multimodal Large Language Models via Solving the Schrödinger Bridge Problem

Ziqiang Shi, Rujie Liu, Shanshan Yu et al.

Recent advancements in Multimodal Large Language Models (MLLMs) have achieved significant success across various domains. However, their use in high-stakes fields like healthcare remains limited due to persistent hallucinations, where generated text contradicts or ignores visual input. We contend that MLLMs can comprehend images but struggle to produce accurate token sequences. Minor perturbations can shift attention from truthful to untruthful states, and the autoregressive nature of text generation often prevents error correction. To address this, we propose SchröMind-a novel framework reducing hallucinations via solving the Schrödinger bridge problem. It establishes a token-level mapping between hallucinatory and truthful activations with minimal transport cost through lightweight training, while preserving the model's original capabilities. Extensive experiments on the POPE and MME benchmarks demonstrate the superiority of Schrödinger, which achieves state-of-the-art performance while introducing only minimal computational overhead.

ASAug 6, 2020Code
Speech Separation Based on Multi-Stage Elaborated Dual-Path Deep BiLSTM with Auxiliary Identity Loss

Ziqiang Shi, Rujie Liu, Jiqing Han

Deep neural network with dual-path bi-directional long short-term memory (BiLSTM) block has been proved to be very effective in sequence modeling, especially in speech separation. This work investigates how to extend dual-path BiLSTM to result in a new state-of-the-art approach, called TasTas, for multi-talker monaural speech separation (a.k.a cocktail party problem). TasTas introduces two simple but effective improvements, one is an iterative multi-stage refinement scheme, and the other is to correct the speech with imperfect separation through a loss of speaker identity consistency between the separated speech and original speech, to boost the performance of dual-path BiLSTM based networks. TasTas takes the mixed utterance of two speakers and maps it to two separated utterances, where each utterance contains only one speaker's voice. Our experiments on the notable benchmark WSJ0-2mix data corpus result in 20.55dB SDR improvement, 20.35dB SI-SDR improvement, 3.69 of PESQ, and 94.86\% of ESTOI, which shows that our proposed networks can lead to big performance improvement on the speaker separation task. We have open sourced our re-implementation of the DPRNN-TasNet here (https://github.com/ShiZiqiang/dual-path-RNNs-DPRNNs-based-speech-separation), and our TasTas is realized based on this implementation of DPRNN-TasNet, it is believed that the results in this paper can be reproduced with ease.

SDJan 23, 2020Code
LaFurca: Iterative Refined Speech Separation Based on Context-Aware Dual-Path Parallel Bi-LSTM

Ziqiang Shi, Rujie Liu, Jiqing Han

Deep neural network with dual-path bi-directional long short-term memory (BiLSTM) block has been proved to be very effective in sequence modeling, especially in speech separation, e.g. DPRNN-TasNet \cite{luo2019dual}. In this paper, we propose several improvements of dual-path BiLSTM based network for end-to-end approach to monaural speech separation. Firstly a dual-path network with intra-parallel BiLSTM and inter-parallel BiLSTM components is introduced to reduce performance sub-variances among different branches. Secondly, we propose to use global context aware inter-intra cross-parallel BiLSTM to further perceive the global contextual information. Finally, a spiral multi-stage dual-path BiLSTM is proposed to iteratively refine the separation results of the previous stages. All these networks take the mixed utterance of two speakers and map it to two separate utterances, where each utterance contains only one speaker's voice. For the objective, we propose to train the network by directly optimizing the utterance level scale-invariant signal-to-distortion ratio (SI-SDR) in a permutation invariant training (PIT) style. Our experiments on the public WSJ0-2mix data corpus results in 20.55dB SDR improvement, 20.35dB SI-SDR improvement, 3.69 of PESQ, and 94.86\% of ESTOI, which shows our proposed networks can lead to performance improvement on the speaker separation task. We have open-sourced our re-implementation of the DPRNN-TasNet in https://github.com/ShiZiqiang/dual-path-RNNs-DPRNNs-based-speech-separation, and our LaFurca is realized based on this implementation of DPRNN-TasNet, it is believed that the results in this paper can be reproduced with ease.

CVFeb 10
Attention to details, logits to truth: visual-aware attention and logits enhancement to mitigate hallucinations in LVLMs

Jingyi Wang, Fei Li, Rujie Liu

Existing Large Vision-Language Models (LVLMs) exhibit insufficient visual attention, leading to hallucinations. To alleviate this problem, some previous studies adjust and amplify visual attention. These methods present a limitation that boosting attention for all visual tokens inevitably increases attention to task irrelevant tokens. To tackle this challenge, we propose a training free attentional intervention algorithm to enhance the attention of task-relevant tokens based on the argument that task-relevant tokens generally demonstrate high visual-textual similarities. Specifically, the vision-text cross-attention submatrices, which represent visual-textual correlations, are extracted to construct the reweighting matrices to reallocate attention. Besides, to enhance the contribution of visual tokens, we inject visual attention values into the beam search decoding to identify solutions with higher visual attention. Extensive experiments demonstrate that this method significantly reduces hallucinations across mainstream LVLMs, while preserving the accuracy and coherence of generated content.

LGApr 19, 2024
Generative Modelling with High-Order Langevin Dynamics

Ziqiang Shi, Rujie Liu

Diffusion generative modelling (DGM) based on stochastic differential equations (SDEs) with score matching has achieved unprecedented results in data generation. In this paper, we propose a novel fast high-quality generative modelling method based on high-order Langevin dynamics (HOLD) with score matching. This motive is proved by third-order Langevin dynamics. By augmenting the previous SDEs, e.g. variance exploding or variance preserving SDEs for single-data variable processes, HOLD can simultaneously model position, velocity, and acceleration, thereby improving the quality and speed of the data generation at the same time. HOLD is composed of one Ornstein-Uhlenbeck process and two Hamiltonians, which reduce the mixing time by two orders of magnitude. Empirical experiments for unconditional image generation on the public data set CIFAR-10 and CelebA-HQ show that the effect is significant in both Frechet inception distance (FID) and negative log-likelihood, and achieves the state-of-the-art FID of 1.85 on CIFAR-10.

CVSep 23, 2020
HiCOMEX: Facial Action Unit Recognition Based on Hierarchy Intensity Distribution and COMEX Relation Learning

Ziqiang Shi, Liu Liu, Zhongling Liu et al.

The detection of facial action units (AUs) has been studied as it has the competition due to the wide-ranging applications thereof. In this paper, we propose a novel framework for the AU detection from a single input image by grasping the \textbf{c}o-\textbf{o}ccurrence and \textbf{m}utual \textbf{ex}clusion (COMEX) as well as the intensity distribution among AUs. Our algorithm uses facial landmarks to detect the features of local AUs. The features are input to a bidirectional long short-term memory (BiLSTM) layer for learning the intensity distribution. Afterwards, the new AU feature continuously passed through a self-attention encoding layer and a continuous-state modern Hopfield layer for learning the COMEX relationships. Our experiments on the challenging BP4D and DISFA benchmarks without any external data or pre-trained models yield F1-scores of 63.7\% and 61.8\% respectively, which shows our proposed networks can lead to performance improvement in the AU detection task.

SDFeb 13, 2020
Hodge and Podge: Hybrid Supervised Sound Event Detection with Multi-Hot MixMatch and Composition Consistence Training

Ziqiang Shi, Liu Liu, Huibin Lin et al.

In this paper, we propose a method called Hodge and Podge for sound event detection. We demonstrate Hodge and Podge on the dataset of Detection and Classification of Acoustic Scenes and Events (DCASE) 2019 Challenge Task 4. This task aims to predict the presence or absence and the onset and offset times of sound events in home environments. Sound event detection is challenging due to the lack of large scale real strongly labeled data. Recently deep semi-supervised learning (SSL) has proven to be effective in modeling with weakly labeled and unlabeled data. This work explores how to extend deep SSL to result in a new, state-of-the-art sound event detection method called Hodge and Podge. With convolutional recurrent neural networks (CRNN) as the backbone network, first, a multi-scale squeeze-excitation mechanism is introduced and added to generate a pyramid squeeze-excitation CRNN. The pyramid squeeze-excitation layer can pay attention to the issue that different sound events have different durations, and to adaptively recalibrate channel-wise spectrogram responses. Further, in order to remedy the lack of real strongly labeled data problem, we propose multi-hot MixMatch and composition consistency training with temporal-frequency augmentation. Our experiments with the public DCASE2019 challenge task 4 validation data resulted in an event-based F-score of 43.4\%, and is about absolutely 1.6\% better than state-of-the-art methods in the challenge. While the F-score of the official baseline is 25.8\%.

SDJul 17, 2019
HODGEPODGE: Sound event detection based on ensemble of semi-supervised learning methods

Ziqiang Shi, Liu Liu, Huibin Lin et al.

In this paper, we present a method called HODGEPODGE\footnotemark[1] for large-scale detection of sound events using weakly labeled, synthetic, and unlabeled data proposed in the Detection and Classification of Acoustic Scenes and Events (DCASE) 2019 challenge Task 4: Sound event detection in domestic environments. To perform this task, we adopted the convolutional recurrent neural networks (CRNN) as our backbone network. In order to deal with a small amount of tagged data and a large amounts of unlabeled in-domain data, we aim to focus primarily on how to apply semi-supervise learning methods efficiently to make full use of limited data. Three semi-supervised learning principles have been used in our system, including: 1) Consistency regularization applies data augmentation; 2) MixUp regularizer requiring that the predictions for a interpolation of two inputs is close to the interpolation of the prediction for each individual input; 3) MixUp regularization applies to interpolation between data augmentations. We also tried an ensemble of various models, which are trained by using different semi-supervised learning principles. Our proposed approach significantly improved the performance of the baseline, achieving the event-based f-measure of 42.0\% compared to 25.8\% event-based f-measure of the baseline in the provided official evaluation dataset. Our submissions ranked third among 18 teams in the task 4.

CVJun 30, 2019
Learning to Find Correlated Features by Maximizing Information Flow in Convolutional Neural Networks

Wei Shen, Fei Li, Rujie Liu

Training convolutional neural networks for image classification tasks usually causes information loss. Although most of the time the information lost is redundant with respect to the target task, there are still cases where discriminative information is also discarded. For example, if the samples that belong to the same category have multiple correlated features, the model may only learn a subset of the features and ignore the rest. This may not be a problem unless the classification in the test set highly depends on the ignored features. We argue that the discard of the correlated discriminative information is partially caused by the fact that the minimization of the classification loss doesn't ensure to learn the overall discriminative information but only the most discriminative information. To address this problem, we propose an information flow maximization (IFM) loss as a regularization term to find the discriminative correlated features. With less information loss the classifier can make predictions based on more informative features. We validate our method on the shiftedMNIST dataset and show the effectiveness of IFM loss in learning representative and discriminative features.

SDFeb 2, 2019
FurcaNet: An end-to-end deep gated convolutional, long short-term memory, deep neural networks for single channel speech separation

Ziqiang Shi, Huibin Lin, Liu Liu et al.

Deep gated convolutional networks have been proved to be very effective in single channel speech separation. However current state-of-the-art framework often considers training the gated convolutional networks in time-frequency (TF) domain. Such an approach will result in limited perceptual score, such as signal-to-distortion ratio (SDR) upper bound of separated utterances and also fail to exploit an end-to-end framework. In this paper we present an integrated simple and effective end-to-end approach to monaural speech separation, which consists of deep gated convolutional neural networks (GCNN) that takes the mixed utterance of two speakers and maps it to two separated utterances, where each utterance contains only one speaker's voice. In addition long short-term memory (LSTM) is employed for long term temporal modeling. For the objective, we propose to train the network by directly optimizing utterance level SDR in a permutation invariant training (PIT) style. Our experiments on the public WSJ0-2mix data corpus demonstrate that this new scheme can produce more discriminative separated utterances and leading to performance improvement on the speaker separation task.

SDFeb 2, 2019
Is CQT more suitable for monaural speech separation than STFT? an empirical study

Ziqiang Shi, Huibin Lin, Liu Liu et al.

Short-time Fourier transform (STFT) is used as the front end of many popular successful monaural speech separation methods, such as deep clustering (DPCL), permutation invariant training (PIT) and their various variants. Since the frequency component of STFT is linear, while the frequency distribution of human auditory system is nonlinear. In this work we propose and give an empirical study to use an alternative front end called constant Q transform (CQT) instead of STFT to achieve a better simulation of the frequency resolving power of the human auditory system. The upper bound in signal-to-distortion (SDR) of ideal speech separation based on CQT's ideal ration mask (IRM) is higher than that based on STFT. In the same experimental setting on WSJ0-2mix corpus, we examined the performance of CQT under different backends, including the original DPCL, utterance level PIT, and some of their variants. It is found that all CQT-based methods are better than STFT-based methods, and achieved on average 0.4dB better performance than STFT based method in SDR improvements.

CVDec 5, 2018
Learning to generate filters for convolutional neural networks

Wei Shen, Rujie Liu

Conventionally, convolutional neural networks (CNNs) process different images with the same set of filters. However, the variations in images pose a challenge to this fashion. In this paper, we propose to generate sample-specific filters for convolutional layers in the forward pass. Since the filters are generated on-the-fly, the model becomes more flexible and can better fit the training data compared to traditional CNNs. In order to obtain sample-specific features, we extract the intermediate feature maps from an autoencoder. As filters are usually high dimensional, we propose to learn a set of coefficients instead of a set of filters. These coefficients are used to linearly combine the base filters from a filter repository to generate the final filters for a CNN. The proposed method is evaluated on MNIST, MTFL and CIFAR10 datasets. Experiment results demonstrate that the classification accuracy of the baseline model can be improved by using the proposed filter generation method.

CVNov 27, 2018
Tackling Early Sparse Gradients in Softmax Activation Using Leaky Squared Euclidean Distance

Wei Shen, Rujie Liu

Softmax activation is commonly used to output the probability distribution over categories based on certain distance metric. In scenarios like one-shot learning, the distance metric is often chosen to be squared Euclidean distance between the query sample and the category prototype. This practice works well in most time. However, we find that choosing squared Euclidean distance may cause distance explosion leading gradients to be extremely sparse in the early stage of back propagation. We term this phenomena as the early sparse gradients problem. Though it doesn't deteriorate the convergence of the model, it may set up a barrier to further model improvement. To tackle this problem, we propose to use leaky squared Euclidean distance to impose a restriction on distances. In this way, we can avoid distance explosion and increase the magnitude of gradients. Extensive experiments are conducted on Omniglot and miniImageNet datasets. We show that using leaky squared Euclidean distance can improve one-shot classification accuracy on both datasets.

CVNov 27, 2018
Generating Attention from Classifier Activations for Fine-grained Recognition

Wei Shen, Rujie Liu

Recent advances in fine-grained recognition utilize attention maps to localize objects of interest. Although there are many ways to generate attention maps, most of them rely on sophisticated loss functions or complex training processes. In this work, we propose a simple and straightforward attention generation model based on the output activations of classifiers. The advantage of our model is that it can be easily trained with image level labels and softmax loss functions. More specifically, multiple linear local classifiers are firstly adopted to perform fine-grained classification at each location of high level CNN feature maps. The attention map is generated by aggregating and max-pooling the output activations. Then the attention map serves as a surrogate target object mask to train those local classifiers, similar to training models for semantic segmentation. Our model achieves state-of-the-art results on three heavily benchmarked datasets, i.e. 87.9% on CUB-200-2011 dataset, 94.1% on Stanford Cars dataset and 92.1% on FGVC-Aircraft dataset, demonstrating its effectiveness on fine-grained recognition tasks.

SDNov 17, 2017
A Double Joint Bayesian Approach for J-Vector Based Text-dependent Speaker Verification

Ziqiang Shi, Mengjiao Wang, Liu Liu et al.

J-vector has been proved to be very effective in text-dependent speaker verification with short-duration speech. However, the current state-of-the-art back-end classifiers, e.g. joint Bayesian model, cannot make full use of such deep features. In this paper, we generalize the standard joint Bayesian approach to model the multi-faceted information in the j-vector explicitly and jointly. In our generalization, the j-vector was modeled as a result derived by a generative Double Joint Bayesian (DoJoBa) model, which contains several kinds of latent variables. With DoJoBa, we are able to explicitly build a model that can combine multiple heterogeneous information from the j-vectors. In verification step, we calculated the likelihood to describe whether the two j-vectors having consistent labels or not. On the public RSR2015 data corpus, the experimental results showed that our approach can achieve 0.02\% EER and 0.02\% EER for impostor wrong and impostor correct cases respectively.

LGApr 20, 2017
Multi-view (Joint) Probability Linear Discrimination Analysis for Multi-view Feature Verification

Ziqiang Shi, Liu Liu, Mengjiao Wang et al.

Multi-view feature has been proved to be very effective in many multimedia applications. However, the current back-end classifiers cannot make full use of such features. In this paper, we propose a method to model the multi-faceted information in the multi-view features explicitly and jointly. In our approach, the feature was modeled as a result derived by a generative multi-view (joint\footnotemark[1]) Probability Linear Discriminant Analysis (PLDA) model, which contains multiple kinds of latent variables. The usual PLDA model only considers one single label. However, in practical use, when using multi-task learned network as feature extractor, the extracted feature are always attached to several labels. This type of feature is called multi-view feature. With multi-view (joint) PLDA, we are able to explicitly build a model that can combine multiple heterogeneous information from the multi-view features. In verification step, we calculated the likelihood to describe whether the two features having consistent labels or not. This likelihood are used in the following decision-making. Experiments have been conducted on large scale verification task. On the public RSR2015 data corpus, the results showed that our approach can achieve 0.02\% EER and 0.09\% EER for impostor wrong and impostor correct cases respectively.

CVDec 16, 2016
Learning Residual Images for Face Attribute Manipulation

Wei Shen, Rujie Liu

Face attributes are interesting due to their detailed description of human faces. Unlike prior researches working on attribute prediction, we address an inverse and more challenging problem called face attribute manipulation which aims at modifying a face image according to a given attribute value. Instead of manipulating the whole image, we propose to learn the corresponding residual image defined as the difference between images before and after the manipulation. In this way, the manipulation can be operated efficiently with modest pixel modification. The framework of our approach is based on the Generative Adversarial Network. It consists of two image transformation networks and a discriminative network. The transformation networks are responsible for the attribute manipulation and its dual operation and the discriminative network is used to distinguish the generated images from real images. We also apply dual learning to allow transformation networks to learn from each other. Experiments show that residual images can be effectively learned and used for attribute manipulations. The generated images remain most of the details in attribute-irrelevant areas.

OCAug 17, 2016
A better convergence analysis of the block coordinate descent method for large scale machine learning

Ziqiang Shi, Rujie Liu

This paper considers the problems of unconstrained minimization of large scale smooth convex functions having block-coordinate-wise Lipschitz continuous gradients. The block coordinate descent (BCD) method are among the first optimization schemes suggested for solving such problems \cite{nesterov2012efficiency}. We obtain a new lower (to our best knowledge the lowest currently) bound that is $16p^3$ times smaller than the best known on the information-based complexity of BCD method based on an effective technique called Performance Estimation Problem (PEP) proposed by Drori and Teboulle \cite{drori2012performance} recently for analyzing the performance of first-order black box optimization methods. Numerical test confirms our analysis.

LGApr 18, 2016
Empirical study of PROXTONE and PROXTONE$^+$ for Fast Learning of Large Scale Sparse Models

Ziqiang Shi, Rujie Liu

PROXTONE is a novel and fast method for optimization of large scale non-smooth convex problem \cite{shi2015large}. In this work, we try to use PROXTONE method in solving large scale \emph{non-smooth non-convex} problems, for example training of sparse deep neural network (sparse DNN) or sparse convolutional neural network (sparse CNN) for embedded or mobile device. PROXTONE converges much faster than first order methods, while first order method is easy in deriving and controlling the sparseness of the solutions. Thus in some applications, in order to train sparse models fast, we propose to combine the merits of both methods, that is we use PROXTONE in the first several epochs to reach the neighborhood of an optimal solution, and then use the first order method to explore the possibility of sparsity in the following training. We call such method PROXTONE plus (PROXTONE$^+$). Both PROXTONE and PROXTONE$^+$ are tested in our experiments, and which demonstrate both methods improved convergence speed twice as fast at least on diverse sparse model learning problems, and at the same time reduce the size to 0.5\% for DNN models. The source of all the algorithms is available upon request.

NAOct 29, 2014
Online and Stochastic Universal Gradient Methods for Minimizing Regularized Hölder Continuous Finite Sums

Ziqiang Shi, Rujie Liu

Online and stochastic gradient methods have emerged as potent tools in large scale optimization with both smooth convex and nonsmooth convex problems from the classes $C^{1,1}(\reals^p)$ and $C^{1,0}(\reals^p)$ respectively. However to our best knowledge, there is few paper to use incremental gradient methods to optimization the intermediate classes of convex problems with Hölder continuous functions $C^{1,v}(\reals^p)$. In order fill the difference and gap between methods for smooth and nonsmooth problems, in this work, we propose the several online and stochastic universal gradient methods, that we do not need to know the actual degree of smoothness of the objective function in advance. We expanded the scope of the problems involved in machine learning to Hölder continuous functions and to propose a general family of first-order methods. Regret and convergent analysis shows that our methods enjoy strong theoretical guarantees. For the first time, we establish an algorithms that enjoys a linear convergence rate for convex functions that have Hölder continuous gradients.

NAAug 22, 2013
Online and stochastic Douglas-Rachford splitting method for large scale machine learning

Ziqiang Shi, Rujie Liu

Online and stochastic learning has emerged as powerful tool in large scale optimization. In this work, we generalize the Douglas-Rachford splitting (DRs) method for minimizing composite functions to online and stochastic settings (to our best knowledge this is the first time DRs been generalized to sequential version). We first establish an $O(1/\sqrt{T})$ regret bound for batch DRs method. Then we proved that the online DRs splitting method enjoy an $O(1)$ regret bound and stochastic DRs splitting has a convergence rate of $O(1/\sqrt{T})$. The proof is simple and intuitive, and the results and technique can be served as a initiate for the research on the large scale machine learning employ the DRs method. Numerical experiments of the proposed method demonstrate the effectiveness of the online and stochastic update rule, and further confirm our regret and convergence analysis.