Related papers: VC Dimension and Distribution-Free Sample-Based Te…
PAC-learning usually aims to compute a small subset ($\varepsilon$-sample/net) from $n$ items, that provably approximates a given loss function for every query (model, classifier, hypothesis) from a given set of queries, up to an additive…
Multi-index models - functions which only depend on the covariates through a non-linear transformation of their projection on a subspace - are a useful benchmark for investigating feature learning with neural nets. This paper examines the…
Sample complexity of bias estimation is a lower bound on the runtime of any bias detection method. Many regulatory frameworks require the bias to be tested for all subgroups, whose number grows exponentially with the number of protected…
We consider a new learning model in which a joint distribution over vector pairs $(x,y)$ is determined by an unknown function $c(x)$ that maps input vectors $x$ not to individual outputs, but to entire {\em distributions\/} over output…
We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space. Despite the extensive study of function convexity across mathematics, statistics, and computer science, its learnability and…
In machine learning, Domain Adaptation (DA) arises when the distribution gen- erating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is an hard task even under strong assumptions,…
Multi-distribution learning extends agnostic Probably Approximately Correct (PAC) learning to the setting in which a family of $k$ distributions, $\{D_i\}_{i\in[k]}$, is considered and a classifier's performance is measured by its error…
Largest theoretical contribution to Neural Networks comes from VC Dimension which characterizes the sample complexity of classification model in a probabilistic view and are widely used to study the generalization error. So far in the…
Tests based on sample mean vectors and sample spatial signs have been studied in the recent literature for high dimensional data with the dimension larger than the sample size. For suitable sequences of alternatives, we show that the powers…
Koch, Strassle, and Tan [SODA 2023], show that, under the randomized exponential time hypothesis, there is no distribution-free PAC-learning algorithm that runs in time $n^{\tilde O(\log\log s)}$ for the classes of $n$-variable size-$s$…
Deep learning models, including Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs), have achieved state-of-the-art performance on various computer vision tasks such as object classification, detection, segmentation,…
These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…
Due to the costliness of labelled data in real-world applications, semi-supervised object detectors, underpinned by pseudo labelling, are appealing. However, handling confusing samples is nontrivial: discarding valuable confusing samples…
We consider the relationship between learnability of a "base class" of functions on a set $X$, and learnability of a class of statistical functions derived from the base class. For example, we refine results showing that learnability of a…
We study learning problems involving arbitrary classes of functions $F$, distributions $X$ and targets $Y$. Because proper learning procedures, i.e., procedures that are only allowed to select functions in $F$, tend to perform poorly unless…
We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…
Valiant's (2007) model of evolvability models the evolutionary process of acquiring useful functionality as a restricted form of learning from random examples. Linear threshold functions and their various subclasses, such as conjunctions…
Consider the problem of learning a large number of response functions simultaneously based on the same input variables. The training data consist of a single independent random sample of the input variables drawn from a common distribution…
A standard approach in pattern classification is to estimate the distributions of the label classes, and then to apply the Bayes classifier to the estimates of the distributions in order to classify unlabeled examples. As one might expect,…
In practical communication systems, knowledge of channel models is often absent, and consequently, transceivers need be designed based on empirical data. In this work, we study data-driven approaches to reliably choosing decoding metrics…