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Multi-layer feedforward networks have been used to approximate a wide range of nonlinear functions. An important and fundamental problem is to understand the learnability of a network model through its statistical risk, or the expected…

Machine Learning · Computer Science 2022-06-28 Gen Li , Jie Ding

Developing simple, sample-efficient learning algorithms for robust classification is a pressing issue in today's tech-dominated world, and current theoretical techniques requiring exponential sample complexity and complicated improper…

Machine Learning · Computer Science 2023-02-07 Robi Bhattacharjee , Max Hopkins , Akash Kumar , Hantao Yu , Kamalika Chaudhuri

We propose a novel method for selective classification (SC), a problem which allows a classifier to abstain from predicting some instances, thus trading off accuracy against coverage (the fraction of instances predicted). In contrast to…

Machine Learning · Computer Science 2021-10-26 Aditya Gangrade , Anil Kag , Venkatesh Saligrama

We analyze the properties of gradient descent on convex surrogates for the zero-one loss for the agnostic learning of linear halfspaces. If $\mathsf{OPT}$ is the best classification error achieved by a halfspace, by appealing to the notion…

Machine Learning · Computer Science 2021-02-16 Spencer Frei , Yuan Cao , Quanquan Gu

The following critical phenomenon was recently discovered. When a memoryless source is compressed using a variable-length fixed-distortion code, the fastest convergence rate of the (pointwise) compression ratio to the optimal $R(D)$…

Probability · Mathematics 2007-07-13 Amir Dembo , Ioannis Kontoyiannis

Adaptive tomography has been widely investigated to achieve faster state tomography processing of quantum systems. Infidelity of the nearly pure states in a quantum information process generally scales as O(1/sqrt(N) ), which requires a…

Quantum Physics · Physics 2023-05-09 Hyeok Hwang , JaeKyung Choi , Eunseong Kim

While deep neural networks are a highly successful model class, their large memory footprint puts considerable strain on energy consumption, communication bandwidth, and storage requirements. Consequently, model size reduction has become an…

Machine Learning · Statistics 2018-10-02 Marton Havasi , Robert Peharz , José Miguel Hernández-Lobato

We provide an exact non-asymptotic lower bound on the minimax expected excess risk (EER) in the agnostic probably-ap\-proximately-correct (PAC) machine learning classification model and identify minimax learning algorithms as certain…

Machine Learning · Computer Science 2018-01-03 Aryeh Kontorovich , Iosif Pinelis

Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…

Optimization and Control · Mathematics 2024-03-26 Maksim Velikanov , Dmitry Yarotsky

The problem of adaptive noisy clustering is investigated. Given a set of noisy observations $Z_i=X_i+\epsilon_i$, $i=1,...,n$, the goal is to design clusters associated with the law of $X_i$'s, with unknown density $f$ with respect to the…

Statistics Theory · Mathematics 2013-06-11 Michael Chichignoud , Sébastien Loustau

In this paper, we carry out numerical analysis to prove convergence of a novel sample-wise back-propagation method for training a class of stochastic neural networks (SNNs). The structure of the SNN is formulated as discretization of a…

Numerical Analysis · Mathematics 2022-12-20 Richard Archibald , Feng Bao , Yanzhao Cao , Hui Sun

We consider an acceptance-rejection sampler based on a deterministic driver sequence. The deterministic sequence is chosen such that the discrepancy between the empirical target distribution and the target distribution is small. We use…

Statistics Theory · Mathematics 2014-05-06 Houying Zhu , Josef Dick

It is well understood that neural networks with carefully hand-picked weights provide powerful function approximation and that they can be successfully trained in over-parametrized regimes. Since over-parametrization ensures zero training…

Machine Learning · Computer Science 2024-05-21 G. Welper

The Coordinate Ascent Variational Inference scheme is a popular algorithm used to compute the mean-field approximation of a probability distribution of interest. We analyze its random scan version, under log-concavity assumptions on the…

Machine Learning · Statistics 2024-09-24 Hugo Lavenant , Giacomo Zanella

Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…

Optimization and Control · Mathematics 2018-05-22 Mark Cannon

We study the sequential general online regression, known also as the sequential probability assignments, under logarithmic loss when compared against a broad class of experts. We focus on obtaining tight, often matching, lower and upper…

Machine Learning · Computer Science 2023-02-02 Changlong Wu , Mohsen Heidari , Ananth Grama , Wojciech Szpankowski

This study reveals the inherent tolerance of contrastive learning (CL) towards sampling bias, wherein negative samples may encompass similar semantics (\eg labels). However, existing theories fall short in providing explanations for this…

Machine Learning · Computer Science 2023-10-18 Junkang Wu , Jiawei Chen , Jiancan Wu , Wentao Shi , Xiang Wang , Xiangnan He

For many machine learning problems, data is abundant and it may be prohibitive to make multiple passes through the full training set. In this context, we investigate strategies for dynamically increasing the effective sample size, when…

Machine Learning · Computer Science 2016-10-10 Hadi Daneshmand , Aurelien Lucchi , Thomas Hofmann

Deep neural networks (DNNs) suffer from noisy-labeled data because of the risk of overfitting. To avoid the risk, in this paper, we propose a novel DNN training method with sample selection based on adaptive k-set selection, which selects k…

Machine Learning · Computer Science 2021-04-06 H. Song , N. Mitsuo , S. Uchida , D. Suehiro

Let $\Phi$ be a random $k$-CNF formula on $n$ variables and $m$ clauses, where each clause is a disjunction of $k$ literals chosen independently and uniformly. Our goal is to sample an approximately uniform solution of $\Phi$ (or…

Data Structures and Algorithms · Computer Science 2023-06-12 Kun He , Kewen Wu , Kuan Yang