Related papers: How to Shrink Confidence Sets for Many Equivalent …
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
A reliable deep learning system should be able to accurately express its confidence with respect to its predictions, a quality known as calibration. One of the most effective ways to produce reliable confidence estimates with a pre-trained…
For a distribution $p:=\{p_k\}_{k=1}^\infty$ on the positive integers, there are two natural ways to construct a random permutation in $S_n$ or of $\mathbb{N}$ from IID samples from $p$--the $p$-biased construction and the $p$-shifted…
Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…
The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level…
Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
It is not unusual for a data analyst to encounter data sets distributed across several computers. This can happen for reasons such as privacy concerns, efficiency of likelihood evaluations, or just the sheer size of the whole data set. This…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…
We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The…
We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution $p(k)$ of the elements $k$ of a population can be approximated by the…
One of the most fundamental problems in machine learning is to compare examples: Given a pair of objects we want to return a value which indicates degree of (dis)similarity. Similarity is often task specific, and pre-defined distances can…
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…
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-constructive arguments show that F is satisfiable for clause/variable ratios m/n< r(k)~2^k ln 2 with high probability. Yet no efficient algorithm is…
We study the problem of distributed cooperative learning, where a group of agents seeks to agree on a set of hypotheses that best describes a sequence of private observations. In the scenario where the set of hypotheses is large, we propose…
We consider the problem of identifying, from statistics, a distribution of discrete random variables $X_1,\ldots,X_n$ that is a mixture of $k$ product distributions. The best previous sample complexity for $n \in O(k)$ was $(1/\zeta)^{O(k^2…
We establish a connection between distributionally robust optimization (DRO) and classical robust statistics. We demonstrate that this connection arises naturally in the context of estimation under data corruption, where the goal is to…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…