arXiv subjects

Cong Ma

Publications and source records attributed to Cong Ma.

At least 55 records · Page 3Linked to original sources

arXiv2023

Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterization

Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor factorization, one of the most popular approaches is to employ simple iterative algorithms such as gradient descent (GD) to recover the low-rank factors directly, which allow for small memory and computation footprints. However, the convergence rate of GD depends linearly, and sometimes even quadratically, on the condition number of the low-rank object, and therefore, GD slows down painstakingly when the problem is ill-conditioned. This chapter introduces a new algorithmic approach, dubbed scaled gradient descent (ScaledGD), that provably converges linearly at a constant rate independent of the condition number of the low-rank object, while maintaining the low per-iteration cost of gradient descent for a variety of tasks including sensing, robust principal component analysis and completion. In addition, ScaledGD continues to admit fast global convergence to the minimax-optimal solution, again almost independent of the condition number, from a small random initialization when the rank is over-specified in the presence of Gaussian noise. In total, ScaledGD highlights the power of appropriate preconditioning in accelerating nonconvex statistical estimation, where the iteration-varying preconditioners promote desirable invariance properties of the trajectory with respect to the symmetry in low-rank factorization without hurting generalization.

cs.LG↗

arXiv2023

Jump-Start Reinforcement Learning

Reinforcement learning (RL) provides a theoretical framework for continuously improving an agent's behavior via trial and error. However, efficiently learning policies from scratch can be very difficult, particularly for tasks with exploration challenges. In such settings, it might be desirable to initialize RL with an existing policy, offline data, or demonstrations. However, naively performing such initialization in RL often works poorly, especially for value-based methods. In this paper, we present a meta algorithm that can use offline data, demonstrations, or a pre-existing policy to initialize an RL policy, and is compatible with any RL approach. In particular, we propose Jump-Start Reinforcement Learning (JSRL), an algorithm that employs two policies to solve tasks: a guide-policy, and an exploration-policy. By using the guide-policy to form a curriculum of starting states for the exploration-policy, we are able to efficiently improve performance on a set of simulated robotic tasks. We show via experiments that JSRL is able to significantly outperform existing imitation and reinforcement learning algorithms, particularly in the small-data regime. In addition, we provide an upper bound on the sample complexity of JSRL and show that with the help of a guide-policy, one can improve the sample complexity for non-optimism exploration methods from exponential in horizon to polynomial.

cs.LG↗

arXiv2023

Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism

Offline (or batch) reinforcement learning (RL) algorithms seek to learn an optimal policy from a fixed dataset without active data collection. Based on the composition of the offline dataset, two main categories of methods are used: imitation learning which is suitable for expert datasets and vanilla offline RL which often requires uniform coverage datasets. From a practical standpoint, datasets often deviate from these two extremes and the exact data composition is usually unknown a priori. To bridge this gap, we present a new offline RL framework that smoothly interpolates between the two extremes of data composition, hence unifying imitation learning and vanilla offline RL. The new framework is centered around a weak version of the concentrability coefficient that measures the deviation from the behavior policy to the expert policy alone. Under this new framework, we further investigate the question on algorithm design: can one develop an algorithm that achieves a minimax optimal rate and also adapts to unknown data composition? To address this question, we consider a lower confidence bound (LCB) algorithm developed based on pessimism in the face of uncertainty in offline RL. We study finite-sample properties of LCB as well as information-theoretic limits in multi-armed bandits, contextual bandits, and Markov decision processes (MDPs). Our analysis reveals surprising facts about optimality rates. In particular, in all three settings, LCB achieves a faster rate of $1/N$ for nearly-expert datasets compared to the usual rate of $1/\sqrt{N}$ in offline RL, where $N$ is the number of samples in the batch dataset. In the case of contextual bandits with at least two contexts, we prove that LCB is adaptively optimal for the entire data composition range, achieving a smooth transition from imitation learning to offline RL. We further show that LCB is almost adaptively optimal in MDPs.

cs.LG↗

arXiv2023

Optimally tackling covariate shift in RKHS-based nonparametric regression

We study the covariate shift problem in the context of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We focus on two natural families of covariate shift problems defined using the likelihood ratios between the source and target distributions. When the likelihood ratios are uniformly bounded, we prove that the kernel ridge regression (KRR) estimator with a carefully chosen regularization parameter is minimax rate-optimal (up to a log factor) for a large family of RKHSs with regular kernel eigenvalues. Interestingly, KRR does not require full knowledge of likelihood ratios apart from an upper bound on them. In striking contrast to the standard statistical setting without covariate shift, we also demonstrate that a naive estimator, which minimizes the empirical risk over the function class, is strictly sub-optimal under covariate shift as compared to KRR. We then address the larger class of covariate shift problems where the likelihood ratio is possibly unbounded yet has a finite second moment. Here, we propose a reweighted KRR estimator that weights samples based on a careful truncation of the likelihood ratios. Again, we are able to show that this estimator is minimax rate-optimal, up to logarithmic factors.

math.ST↗

arXiv2023

Unraveling Projection Heads in Contrastive Learning: Insights from Expansion and Shrinkage

We investigate the role of projection heads, also known as projectors, within the encoder-projector framework (e.g., SimCLR) used in contrastive learning. We aim to demystify the observed phenomenon where representations learned before projectors outperform those learned after -- measured using the downstream linear classification accuracy, even when the projectors themselves are linear. In this paper, we make two significant contributions towards this aim. Firstly, through empirical and theoretical analysis, we identify two crucial effects -- expansion and shrinkage -- induced by the contrastive loss on the projectors. In essence, contrastive loss either expands or shrinks the signal direction in the representations learned by an encoder, depending on factors such as the augmentation strength, the temperature used in contrastive loss, etc. Secondly, drawing inspiration from the expansion and shrinkage phenomenon, we propose a family of linear transformations to accurately model the projector's behavior. This enables us to precisely characterize the downstream linear classification accuracy in the high-dimensional asymptotic limit. Our findings reveal that linear projectors operating in the shrinkage (or expansion) regime hinder (or improve) the downstream classification accuracy. This provides the first theoretical explanation as to why (linear) projectors impact the downstream performance of learned representations. Our theoretical findings are further corroborated by extensive experiments on both synthetic data and real image data.

stat.ML↗

arXiv2023

Optimal tuning-free convex relaxation for noisy matrix completion

This paper is concerned with noisy matrix completion--the problem of recovering a low-rank matrix from partial and noisy entries. Under uniform sampling and incoherence assumptions, we prove that a tuning-free square-root matrix completion estimator (square-root MC) achieves optimal statistical performance for solving the noisy matrix completion problem. Similar to the square-root Lasso estimator in high-dimensional linear regression, square-root MC does not rely on the knowledge of the size of the noise. While solving square-root MC is a convex program, our statistical analysis of square-root MC hinges on its intimate connections to a nonconvex rank-constrained estimator.

math.ST↗

arXiv2023

E2TIMT: Efficient and Effective Modal Adapter for Text Image Machine Translation

Text image machine translation (TIMT) aims to translate texts embedded in images from one source language to another target language. Existing methods, both two-stage cascade and one-stage end-to-end architectures, suffer from different issues. The cascade models can benefit from the large-scale optical character recognition (OCR) and MT datasets but the two-stage architecture is redundant. The end-to-end models are efficient but suffer from training data deficiency. To this end, in our paper, we propose an end-to-end TIMT model fully making use of the knowledge from existing OCR and MT datasets to pursue both an effective and efficient framework. More specifically, we build a novel modal adapter effectively bridging the OCR encoder and MT decoder. End-to-end TIMT loss and cross-modal contrastive loss are utilized jointly to align the feature distribution of the OCR and MT tasks. Extensive experiments show that the proposed method outperforms the existing two-stage cascade models and one-stage end-to-end models with a lighter and faster architecture. Furthermore, the ablation studies verify the generalization of our method, where the proposed modal adapter is effective to bridge various OCR and MT models.

cs.CL↗

arXiv2023

Multi-Teacher Knowledge Distillation For Text Image Machine Translation

Text image machine translation (TIMT) has been widely used in various real-world applications, which translates source language texts in images into another target language sentence. Existing methods on TIMT are mainly divided into two categories: the recognition-then-translation pipeline model and the end-to-end model. However, how to transfer knowledge from the pipeline model into the end-to-end model remains an unsolved problem. In this paper, we propose a novel Multi-Teacher Knowledge Distillation (MTKD) method to effectively distillate knowledge into the end-to-end TIMT model from the pipeline model. Specifically, three teachers are utilized to improve the performance of the end-to-end TIMT model. The image encoder in the end-to-end TIMT model is optimized with the knowledge distillation guidance from the recognition teacher encoder, while the sequential encoder and decoder are improved by transferring knowledge from the translation sequential and decoder teacher models. Furthermore, both token and sentence-level knowledge distillations are incorporated to better boost the translation performance. Extensive experimental results show that our proposed MTKD effectively improves the text image translation performance and outperforms existing end-to-end and pipeline models with fewer parameters and less decoding time, illustrating that MTKD can take advantage of both pipeline and end-to-end models.

cs.CL↗

arXiv2023

A Local Concentration-based Descriptor Predicting the Stacking Fault Energy of Refractory High Entropy Alloys

Stacking fault energy (SFE) is an essential parameter for characterizing mechanical properties. However, in high entropy alloys (HEAs), the local chemical environment varies significantly across different stacking fault planes, resulting in a substantial fluctuation of SFE values rather than a unique value, which prohibits the prediction of the local SFE. Herein, we proposed an effective descriptor based on the local concentration ratio near stacking fault to quantitatively predict the local SFE of refractory HEAs. We find that the role of a given element in determining SFE strongly depends on its valence-electron number relative to other components and the contribution of its s- and d-electrons to its cohesive properties, which can be understood in the framework of the tight-binding model. Notably, the descriptor not only unifies the local nature of SFE from simple alloys to HEAs but also helps to quickly design HEAs as the involved parameters are easily accessible.

cond-mat.mtrl-sci↗

arXiv2023

Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descent

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key challenge is to develop computationally efficient and provably correct algorithms for extracting useful information from tensor data that are simultaneously robust to corruptions and ill-conditioning. This paper tackles tensor robust principal component analysis (RPCA), which aims to recover a low-rank tensor from its observations contaminated by sparse corruptions, under the Tucker decomposition. To minimize the computation and memory footprints, we propose to directly recover the low-dimensional tensor factors -- starting from a tailored spectral initialization -- via scaled gradient descent (ScaledGD), coupled with an iteration-varying thresholding operation to adaptively remove the impact of corruptions. Theoretically, we establish that the proposed algorithm converges linearly to the true low-rank tensor at a constant rate that is independent with its condition number, as long as the level of corruptions is not too large. Empirically, we demonstrate that the proposed algorithm achieves better and more scalable performance than state-of-the-art matrix and tensor RPCA algorithms through synthetic experiments and real-world applications.

stat.ML↗

arXiv2023

$O(T^{-1})$ Convergence of Optimistic-Follow-the-Regularized-Leader in Two-Player Zero-Sum Markov Games

We prove that optimistic-follow-the-regularized-leader (OFTRL), together with smooth value updates, finds an $O(T^{-1})$-approximate Nash equilibrium in $T$ iterations for two-player zero-sum Markov games with full information. This improves the $\tilde{O}(T^{-5/6})$ convergence rate recently shown in the paper Zhang et al (2022). The refined analysis hinges on two essential ingredients. First, the sum of the regrets of the two players, though not necessarily non-negative as in normal-form games, is approximately non-negative in Markov games. This property allows us to bound the second-order path lengths of the learning dynamics. Second, we prove a tighter algebraic inequality regarding the weights deployed by OFTRL that shaves an extra $\log T$ factor. This crucial improvement enables the inductive analysis that leads to the final $O(T^{-1})$ rate.

cs.LG↗

arXiv2022

Improving End-to-End Text Image Translation From the Auxiliary Text Translation Task

End-to-end text image translation (TIT), which aims at translating the source language embedded in images to the target language, has attracted intensive attention in recent research. However, data sparsity limits the performance of end-to-end text image translation. Multi-task learning is a non-trivial way to alleviate this problem via exploring knowledge from complementary related tasks. In this paper, we propose a novel text translation enhanced text image translation, which trains the end-to-end model with text translation as an auxiliary task. By sharing model parameters and multi-task training, our model is able to take full advantage of easily-available large-scale text parallel corpus. Extensive experimental results show our proposed method outperforms existing end-to-end methods, and the joint multi-task learning with both text translation and recognition tasks achieves better results, proving translation and recognition auxiliary tasks are complementary.

cs.CL↗

arXiv2022

Pessimism for Offline Linear Contextual Bandits using $\ell_p$ Confidence Sets

We present a family $\{\hatπ\}_{p\ge 1}$ of pessimistic learning rules for offline learning of linear contextual bandits, relying on confidence sets with respect to different $\ell_p$ norms, where $\hatπ_2$ corresponds to Bellman-consistent pessimism (BCP), while $\hatπ_\infty$ is a novel generalization of lower confidence bound (LCB) to the linear setting. We show that the novel $\hatπ_\infty$ learning rule is, in a sense, adaptively optimal, as it achieves the minimax performance (up to log factors) against all $\ell_q$-constrained problems, and as such it strictly dominates all other predictors in the family, including $\hatπ_2$.

cs.LG↗

arXiv2022

Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurements

Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is to faithfully recover the tensor from highly incomplete measurements in a statistically and computationally efficient manner. Harnessing the low-rank structure of tensors in the Tucker decomposition, this paper develops a scaled gradient descent (ScaledGD) algorithm to directly recover the tensor factors with tailored spectral initializations, and shows that it provably converges at a linear rate independent of the condition number of the ground truth tensor for two canonical problems -- tensor completion and tensor regression -- as soon as the sample size is above the order of $n^{3/2}$ ignoring other parameter dependencies, where $n$ is the dimension of the tensor. This leads to an extremely scalable approach to low-rank tensor estimation compared with prior art, which suffers from at least one of the following drawbacks: extreme sensitivity to ill-conditioning, high per-iteration costs in terms of memory and computation, or poor sample complexity guarantees. To the best of our knowledge, ScaledGD is the first algorithm that achieves near-optimal statistical and computational complexities simultaneously for low-rank tensor completion with the Tucker decomposition. Our algorithm highlights the power of appropriate preconditioning in accelerating nonconvex statistical estimation, where the iteration-varying preconditioners promote desirable invariance properties of the trajectory with respect to the underlying symmetry in low-rank tensor factorization.

cs.LG↗

arXiv2022

A new similarity measure for covariate shift with applications to nonparametric regression

We study covariate shift in the context of nonparametric regression. We introduce a new measure of distribution mismatch between the source and target distributions that is based on the integrated ratio of probabilities of balls at a given radius. We use the scaling of this measure with respect to the radius to characterize the minimax rate of estimation over a family of Hölder continuous functions under covariate shift. In comparison to the recently proposed notion of transfer exponent, this measure leads to a sharper rate of convergence and is more fine-grained. We accompany our theory with concrete instances of covariate shift that illustrate this sharp difference.

math.ST↗

arXiv2022

BBA-net: A bi-branch attention network for crowd counting

In the field of crowd counting, the current mainstream CNN-based regression methods simply extract the density information of pedestrians without finding the position of each person. This makes the output of the network often found to contain incorrect responses, which may erroneously estimate the total number and not conducive to the interpretation of the algorithm. To this end, we propose a Bi-Branch Attention Network (BBA-NET) for crowd counting, which has three innovation points. i) A two-branch architecture is used to estimate the density information and location information separately. ii) Attention mechanism is used to facilitate feature extraction, which can reduce false responses. iii) A new density map generation method combining geometric adaptation and Voronoi split is introduced. Our method can integrate the pedestrian's head and body information to enhance the feature expression ability of the density map. Extensive experiments performed on two public datasets show that our method achieves a lower crowd counting error compared to other state-of-the-art methods.

cs.CV↗

arXiv2022

The design of a time-interleaved analog-digital conversion modulator based on FPGA-TDC for PET application

Fully Field Programmable Gate Array (FPGA)based digitizer for high-resolution time and energy measurement is an attractive low cost solution for the readout electronics in positron emission computed tomography (PET)detector. In recent years, the FPGA based time-digital converter (FPGA-TDC) has been widely used for time measurement in the commercial PET scanners. Yet, for the energy measurement, few studies have been reported on a fully FPGA based, large dynamic range and high resolution alternative to the commercial analog-digital converter (ADC). Our previous research presents a 25 Ms/s FPGA-TDC based free-running ADC (FPGA-ADC), and successfully employed it in the readout electronics for PET detector. In this work-in-progress study, by means of the time-interleaved strategy, a 50 Ms/s FPGA-ADC is presented. With only two off-chip resistors, both the A/D conversion and energy measurement are achieved on a Xilinx Kintex-7 FPGA. Therefore, this method has great advantages inimproving system integration. Initial performance tests are also presented, and we hope it can give us a possibility to develop a new FPGA-only front-end digitizer for PET in future.

physics.ins-det↗

arXiv2022

An FPGA Based energy correction method for one-to-one coupled PET detector: model and evaluation

A PET scanner based on silicon photomultipliers (SiPMs) has been widely used as an advanced nuclear medicine imaging technique that yields quantitative images of regional in vivo biology and biochemistry. The compact size of the SiPM allows direct one to one coupling between the scintillation crystal and the photosensor, yielding better timing and energy resolutions than the light sharing methods that have to be used in photomultiplier tube (PMT) PET systems. To decrease the volume of readout electronics, a front end multiplexer with position decoder is a common choice for the one to one system without a highly integrated application specific integrated circuit (ASIC). However, in this case we cannot measure each crystal's deposited energy inspired by an annihilation photon, so the inter-crystal scatter (ICS) events will lead to the crystal mispositioning and then deteriorate the detector intrinsic resolution. Besides, considering the events rejection within the energy window resulting from the gain dispersion and nonlinear outputs of the SiPMs, an energy correction mechanism is needed. Yet, lack of the information of each crystal's energy will introduce large energy correction error for the ICS events. For this issue, an online energy correction mechanism implemented on a Kintext-7 Field Programmable Gate Array (FPGA) device is presented in this paper. Experiments in the laboratory were performed using an 8 x 8 segmented LYSO crystals coupled with an 8 x 8 SiPM (J-series, from ON Semiconductor) array which is under 22Na point source excitation. Test results indicate that both the energy of the non-ICS and ICS events can be precisely corrected and the energy resolution is better than 12 %. We also applied this method to an actual clinical PET scanner under a 68Ge line source to verify its multi-channel reliability.

physics.ins-det↗