34 accepted papers
Asynchronous stochastic gradient descent (ASGD) is widely adopted in distributed and federated learning. In this paper, we develop a sharp generalization analysis for ASGD by leveraging the concept of on-average model stability. For convex and smooth objectives, we establish stability and excess ris…
In this paper, we present generalization bounds for the unsupervised risk in the Deep Contrastive Representation Learning framework, which employs deep neural networks as representation functions. We approach this problem from two angles. On the one hand, we derive a parameter-counting bound that sc…
It has been recently observed in much of the literature that neural networks exhibit a bottleneck rank property: for larger depths, the activation and weights of neural networks trained with gradient-based methods tend to be of approximately low rank. In fact, the rank of the activations of each lay…
We consider a PAC-Bayes analysis of stochastic optimization algorithms, and devise a new SGDA algorithm inspired from our bounds. Our algorithm learns a data-dependent sampling scheme along with model parameters, which may be seen as assigning a probability to each training point. We demonstrate tha
We study the discriminative probabilistic modeling on a continuous domain for the data prediction task of (multimodal) self-supervised representation learning. To address the challenge of computing the integral in the partition function for each anchor data, we leverage the multiple importance sampl…
Recent advances have significantly improved our understanding of the generalization performance of gradient descent (GD) methods in deep neural networks. A natural and fundamental question is whether GD can achieve generalization rates comparable to the minimax optimal rates established in the kerne…
Decentralized SGD (D-SGD) is a popular optimization method to train large-scale machine learning models. In this paper, we study the generalization behavior of D-SGD for both smooth and nonsmooth problems by leveraging the algorithm stability. For convex and smooth problems, we develop stability bou…
Pairwise learning includes various machine learning tasks, with ranking and metric learning serving as the primary representatives. While randomized coordinate descent (RCD) is popular in various problems, there is much less theoretical analysis on the generalization behavior of models trained by RC…
The Alternating Direction Method of Multipliers (ADMM) has gained significant attention across a broad spectrum of machine learning applications. Incorporating the over-relaxation technique shows potential for enhancing the convergence rate of ADMM. However, determining optimal algorithmic parameter…
Recently, contrastive learning has found impressive success in advancing the state of the art in solving various machine learning tasks. However, the existing generalization analysis is very limited or even not meaningful. In particular, the existing generalization error bounds depend linearly on th…
We study inductive matrix completion (matrix completion with side information) under an i.i.d. subgaussian noise assumption at a low noise regime, with uniform sampling of the entries. We obtain for the first time generalization bounds with the following three properties: (1) they scale like the s…
Generalization analysis of learning algorithms often builds on a critical assumption that training examples are independently and identically distributed, which is often violated in practical problems such as time series prediction. In this paper, we use algorithmic stability to study the generaliza…
We give sharper bounds for uniformly stable randomized algorithms in a PAC-Bayesian framework, which improve the existing results by up to a factor of $\sqrt{n}$ (ignoring a log factor), where $n$ is the sample size. The key idea is to bound the moment generating function of the generalization gap u…
In distributed training of deep neural networks, people usually run Stochastic Gradient Descent (SGD) or its variants on each machine and communicate with other machines periodically. However, SGD might converge slowly in training some deep neural networks (e.g., RNN, LSTM) because of the exploding…
Stochastic gradient descent ascent (SGDA) and its variants have been the workhorse for solving minimax problems. However, in contrast to the well-studied stochastic gradient descent (SGD) with differential privacy (DP) constraints, there is little work on understanding the generalization (utility…
Many recent studies have highlighted the susceptibility of virtually all machine-learning models to adversarial attacks. Adversarial attacks are imperceptible changes to an input example of a given prediction model. Such changes are carefully designed to alter the otherwise correct prediction of the…
While significant theoretical progress has been achieved, unveiling the generalization mystery of overparameterized neural networks still remains largely elusive. In this paper, we study the generalization behavior of shallow neural networks (SNNs) by leveraging the concept of algorithmic stability…
Recently there is a large amount of work devoted to the study of Markov chain stochastic gradient methods (MC-SGMs) which mainly focus on their convergence analysis for solving minimization problems. In this paper, we provide a comprehensive generalization analysis of MC-SGMs for both minimization…
In this paper, we bridge the gap between the state-of-the-art theoretical results for matrix completion with the nuclear norm and their equivalent in \textit{inductive matrix completion}: (1) In the distribution-free setting, we prove bounds improving the previously best scaling of $O(rd^2)$ to $\wi…
In machine learning we often encounter structured output prediction problems (SOPPs), i.e. problems where the output space admits a rich internal structure. Application domains where SOPPs naturally occur include natural language processing, speech recognition, and computer vision. Typical SOPPs hav…
Many fundamental machine learning tasks can be formulated as a problem of learning with vector-valued functions, where we learn multiple scalar-valued functions together. Although there is some generalization analysis on different specific algorithms under the empirical risk minimization principle,…
Recently, there is a growing interest in studying pairwise learning since it includes many important machine learning tasks as specific examples, e.g., metric learning, AUC maximization and ranking. While stochastic gradient descent (SGD) is an efficient method, there is a lacking study on its gener…
We propose a novel training methodology---Concept Group Learning (CGL)---that encourages training of interpretable CNN filters by partitioning filters in each layer into \emph{concept groups}, each of which is trained to learn a single visual concept. We achieve this through a novel regularization s…
We show generalisation error bounds for deep learning with two main improvements over the state of the art. (1) Our bounds have no explicit dependence on the number of classes except for logarithmic factors. This holds even when formulating the bounds in terms of the Frobenius-norm of the weight mat…
Stochastic optimization has become the workhorse behind many successful machine learning applications, which motivates a lot of theoretical analysis to understand its empirical behavior. As a comparison, there is far less work to study the generalization behavior especially in a non-convex learning…
Pairwise learning refers to learning tasks where the loss function depends on a pair of instances. It instantiates many important machine learning tasks such as bipartite ranking and metric learning. A popular approach to handle streaming data in pairwise learning is an online gradient descent (OG…
Pairwise learning has recently received increasing attention since it subsumes many important machine learning tasks (e.g. AUC maximization and metric learning) into a unifying framework. In this paper, we give the first-ever-known stability and generalization analysis of stochastic gradient descent…
Randomized coordinate descent (RCD) is a popular optimization algorithm with wide applications in various machine learning problems, which motivates a lot of theoretical analysis on its convergence behavior. As a comparison, there is no work studying how the models trained by RCD would generalize to…
Many machine learning problems can be formulated as minimax problems such as Generative Adversarial Networks (GANs), AUC maximization and robust estimation, to mention but a few. A substantial amount of studies are devoted to studying the convergence behavior of their stochastic gradient-type algori…
Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions on the boundedness of gradients, smoothness and convexity o…
Pairwise learning refers to learning tasks with loss functions depending on a pair of training examples, which includes ranking and metric learning as specific examples. Recently, there has been an increasing amount of attention on the generalization analysis of pairwise learning to understand its p…
Stochastic composite mirror descent (SCMD) is a simple and efficient method able to capture both geometric and composite structures of optimization problems in machine learning. Existing strategies require to take either an average or a random selection of iterates to achieve optimal convergence rat…
We study stochastic composite mirror descent, a class of scalable algorithms able to exploit the geometry and composite structure of a problem. We consider both convex and strongly convex objectives with non-smooth loss functions, for each of which we establish high-probability convergence rates opt…
This paper studies the generalization performance of multi-class classification algorithms, for which we obtain, for the first time, a data-dependent generalization error bound with a logarithmic dependence on the class size, substantially improving the state-of-the-art linear dependence in the exis…