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In recent years, deep learning researchers have focused on how to find the interpretability behind deep learning models. However, today cognitive competence of human has not completely covered the deep learning model. In other words, there…

Machine Learning · Computer Science 2018-12-04 Jinwei Zhao , Qizhou Wang , Yufei Wang , Xinhong Hei , Yu Liu

A major challenge in modern machine learning is theoretically understanding the generalization properties of overparameterized models. Many existing tools rely on uniform convergence (UC), a property that, when it holds, guarantees that the…

Machine Learning · Computer Science 2023-03-14 Margalit Glasgow , Colin Wei , Mary Wootters , Tengyu Ma

Standard uniform convergence results bound the generalization gap of the expected loss over a hypothesis class. The emergence of risk-sensitive learning requires generalization guarantees for functionals of the loss distribution beyond the…

Machine Learning · Statistics 2022-06-29 Liu Leqi , Audrey Huang , Zachary C. Lipton , Kamyar Azizzadenesheli

Adversarially trained models exhibit a large generalization gap: they can interpolate the training set even for large perturbation radii, but at the cost of large test error on clean samples. To investigate this gap, we decompose the test…

Machine Learning · Computer Science 2021-06-15 Yaodong Yu , Zitong Yang , Edgar Dobriban , Jacob Steinhardt , Yi Ma

In various applications of regression analysis, in addition to errors in the dependent observations also errors in the predictor variables play a substantial role and need to be incorporated in the statistical modeling process. In this…

Statistics Theory · Mathematics 2020-09-03 Katharina Proksch , Nicolai Bissantz , Hajo Holzmann

Error probabilities of random codes for memoryless channels are considered in this paper. In the area of communication systems, admissible error probability is very small and it is sometimes more important to discuss the relative gap…

Information Theory · Computer Science 2015-06-11 Junya Honda

At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…

Machine Learning · Computer Science 2020-05-04 Melikasadat Emami , Mojtaba Sahraee-Ardakan , Parthe Pandit , Sundeep Rangan , Alyson K. Fletcher

In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…

Information Theory · Computer Science 2022-06-22 Tomer Berg , Or Ordentlich , Ofer Shayevitz

We prove a new generalization bound that shows for any class of linear predictors in Gaussian space, the Rademacher complexity of the class and the training error under any continuous loss $\ell$ can control the test error under all Moreau…

Machine Learning · Statistics 2022-10-24 Lijia Zhou , Frederic Koehler , Pragya Sur , Danica J. Sutherland , Nathan Srebro

Overparameterized models that achieve zero training error are observed to generalize well on average, but degrade in performance when faced with data that is under-represented in the training sample. In this work, we study an…

Machine Learning · Statistics 2024-05-13 Kuo-Wei Lai , Vidya Muthukumar

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

Probability · Mathematics 2022-09-29 Damjan Škulj

Deep learning methods operate in regimes that defy the traditional statistical mindset. Neural network architectures often contain more parameters than training samples, and are so rich that they can interpolate the observed labels, even if…

Statistics Theory · Mathematics 2020-12-14 Song Mei , Andrea Montanari

We study a localized notion of uniform convergence known as an "optimistic rate" (Panchenko 2002; Srebro et al. 2010) for linear regression with Gaussian data. Our refined analysis avoids the hidden constant and logarithmic factor in…

Machine Learning · Statistics 2021-12-09 Lijia Zhou , Frederic Koehler , Danica J. Sutherland , Nathan Srebro

Within the framework of on-line learning, we study the generalization error of an ensemble learning machine learning from a linear teacher perceptron. The generalization error achieved by an ensemble of linear perceptrons having homogeneous…

Disordered Systems and Neural Networks · Physics 2009-11-10 Kazuyuki Hara , Masato Okada

We propose to study the generalization error of a learned predictor $\hat h$ in terms of that of a surrogate (potentially randomized) predictor that is coupled to $\hat h$ and designed to trade empirical risk for control of generalization…

Machine Learning · Computer Science 2021-09-13 Jeffrey Negrea , Gintare Karolina Dziugaite , Daniel M. Roy

In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…

Data Structures and Algorithms · Computer Science 2017-08-17 Tuğkan Batu , Clément L. Canonne

Calibration is a fundamental property of a good predictive model: it requires that the model predicts correctly in proportion to its confidence. Modern neural networks, however, provide no strong guarantees on their calibration -- and can…

Machine Learning · Computer Science 2022-10-07 A. Michael Carrell , Neil Mallinar , James Lucas , Preetum Nakkiran

Existing generalization theories of supervised learning typically take a holistic approach and provide bounds for the expected generalization over the whole data distribution, which implicitly assumes that the model generalizes similarly…

Machine Learning · Computer Science 2024-01-08 Firas Laakom , Yuheng Bu , Moncef Gabbouj

An interpolation error is an integral of the squared error of a regression model over a domain of interest. We consider the interpolation error for the case of misspecified Gaussian process regression: used covariance function differs from…

Statistics Theory · Mathematics 2018-03-28 A. Zaytsev , E. Romanenkova , D. Ermilov

This manuscript considers the problem of learning a random Gaussian network function using a fully connected network with frozen intermediate layers and trainable readout layer. This problem can be seen as a natural generalization of the…

Machine Learning · Statistics 2023-02-02 Dominik Schröder , Hugo Cui , Daniil Dmitriev , Bruno Loureiro