Related papers: Exact Gap between Generalization Error and Uniform…
Recent works have investigated the sample complexity necessary for fair machine learning. The most advanced of such sample complexity bounds are developed by analyzing multicalibration uniform convergence for a given predictor class. We…
In randomised trials, continuous endpoints are often measured with some degree of error. This study explores the impact of ignoring measurement error, and proposes methods to improve statistical inference in the presence of measurement…
This paper focuses on understanding how the generalization error scales with the amount of the training data for deep neural networks (DNNs). Existing techniques in statistical learning require computation of capacity measures, such as VC…
This paper deals with probabilistic upper bounds for the error in functional estimation defined on some interpolation and extrapolation designs, when the function to estimate is supposed to be analytic. The error pertaining to the estimate…
We study the generalization capability of nearly-interpolating linear regressors: $\boldsymbol{\beta}$'s whose training error $\tau$ is positive but small, i.e., below the noise floor. Under a random matrix theoretic assumption on the data…
Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…
We investigate the expressive power of deep residual neural networks idealized as continuous dynamical systems through control theory. Specifically, we consider two properties that arise from supervised learning, namely universal…
Transductive conformal prediction addresses the simultaneous prediction for multiple data points. Given a desired confidence level, the objective is to construct a prediction set that includes the true outcomes with the prescribed…
One fundamental goal in any learning algorithm is to mitigate its risk for overfitting. Mathematically, this requires that the learning algorithm enjoys a small generalization risk, which is defined either in expectation or in probability.…
King and Roberts (2015, KR) claim that a disagreement between robust and classical standard errors exposes model misspecification. We emphasize that KR's claim only generally applies to parametric models: models that assume a restrictive…
Sensitivity analysis for measurement error can be applied in the absence of validation data by means of regression calibration and simulation-extrapolation. These have not been compared for this purpose. A simulation study was conducted…
Understanding how the test risk scales with model complexity is a central question in machine learning. Classical theory is challenged by the learning curves observed for large over-parametrized deep networks. Capacity measures based on…
We study the problem of generalized uniformity testing \cite{BC17} of a discrete probability distribution: Given samples from a probability distribution $p$ over an {\em unknown} discrete domain $\mathbf{\Omega}$, we want to distinguish,…
Deep learning is renowned for its theory-practice gap, whereby principled theory typically fails to provide much beneficial guidance for implementation in practice. This has been highlighted recently by the benign overfitting phenomenon:…
We introduce a new notion of generalization -- Distributional Generalization -- which roughly states that outputs of a classifier at train and test time are close *as distributions*, as opposed to close in just their average error. For…
We study the problem of learning causal models from observational data through the lens of interpolation and its counterpart -- regularization. A large volume of recent theoretical, as well as empirical work, suggests that, in highly…
An evolving line of machine learning works observe empirical evidence that suggests interpolating estimators -- the ones that achieve zero training error -- may not necessarily be harmful. This paper pursues theoretical understanding for an…
When training neural networks as classifiers, it is common to observe an increase in average test loss while still maintaining or improving the overall classification accuracy on the same dataset. In spite of the ubiquity of this…
Conformal prediction, which makes no distributional assumptions about the data, has emerged as a powerful and reliable approach to uncertainty quantification in practical applications. The nonconformity measure used in conformal prediction…
This paper is motivated by an open problem around deep networks, namely, the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data. In this paper, we analyze this phenomenon in…