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Neural scaling laws suggest that the test error of large language models trained online decreases polynomially as the model size and data size increase. However, such scaling can be unsustainable when running out of new data. In this work,…
Modern generative and vision-language models (VLMs) are increasingly used in scientific and medical decision support, where predicted probabilities must be both accurate and well calibrated. Despite strong empirical results with moderate…
We develop a skew-adaptive extension of split conformal prediction for regression. The method starts from an asymmetric interval family centered at a point prediction and uses the gauge approach to deduce the conformity score induced by…
Given n observations, we study the consistency of a batch of k new observations, in terms of their distribution function. We propose a non-parametric, non-likelihood test based on Edgeworth expansion of the distribution function. The…
We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models for large data, in which the access to the data is restricted in some way. Our…
As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate…
Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
Confidence sets play a fundamental role in statistical inference. In this paper, we consider confidence intervals for high dimensional linear regression with random design. We first establish the convergence rates of the minimax expected…
The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big data analysis. We propose an orthogonal…
The finite sensitivity of instruments or detection methods means that data sets in many areas of astronomy, for example cosmological or exoplanet surveys, are necessarily systematically incomplete. Such data sets, where the population being…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
Intuitively, one would expect accuracy of a trained neural network's prediction on test samples to correlate with how densely the samples are surrounded by seen training samples in representation space. We find that a bound on empirical…
Deep neural network training often involves stochastic optimization, meaning each run will produce a different model. This implies that hyperparameters of the training process, such as the random seed itself, can potentially have…
With the progress of information technology, large amounts of asymmetric, leptokurtic and heavy-tailed data are arising in various fields, such as finance, engineering, genetics and medicine. It is very challenging to model those kinds of…
Regression splines are largely used to investigate and predict data behavior, attracting the interest of mathematicians for their beautiful numerical properties, and of statisticians for their versatility with respect to the applications.…
We study the basic statistical problem of testing whether normally distributed $n$-dimensional data has been truncated, i.e. altered by only retaining points that lie in some unknown truncation set $S \subseteq \mathbb{R}^n$. As our main…
The goal of regression analysis is to predict the value of a numeric outcome variable y given a vector of joint values of other (predictor) variables x. Usually a particular x-vector does not specify a repeatable value for y, but rather a…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
Real-life data are often non-IID due to complex distributions and interactions, and the sensitivity to the distribution of samples can differ among learning models. Accordingly, a key question for any supervised or unsupervised model is…
We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given $n$ i.i.d. samples from the distribution…