Related papers: A note on the relation between XOR and Selective X…
This paper deals with strong invariance principles (known also as strong approximation theorems) for sums of the form $\sum_{n=1}^{[Nt]}F\big(X(n),X(2n),...,X(kn), X(q_{k+1}(n)),X(q_{k+2}(n)),..., X(q_\ell(n))\big)$
In this paper we motivate the causal mechanisms behind sample selection induced collider bias (selection collider bias) that can cause Large Language Models (LLMs) to learn unconditional dependence between entities that are unconditionally…
This paper develops a rigorous argument for why the use of Shapley values in explainable AI (XAI) will necessarily yield provably misleading information about the relative importance of features for predictions. Concretely, this paper…
In a binary classification problem the feature vector (predictor) is the input to a scoring function that produces a decision value (score), which is compared to a particular chosen threshold to provide a final class prediction (output).…
Time series forecasting aids decision-making, especially for stakeholders who rely on accurate predictions, making it very important to understand and explain these models to ensure informed decisions. Traditional explainable AI (XAI)…
We consider the problem of computing the measure of a regular language of infinite binary trees. While the general case remains unsolved, we show that the measure of a language defined by a first-order formula with no descendant relation or…
Budget feasible mechanism design studies procurement combinatorial auctions where the sellers have private costs to produce items, and the buyer(auctioneer) aims to maximize a social valuation function on subsets of items, under the budget…
We study the relative-error property testing model for Boolean functions that was recently introduced in the work of Chen et al. (SODA 2025). In relative-error testing, the testing algorithm gets uniform random satisfying assignments as…
The randomized query complexity $R(f)$ of a boolean function $f\colon\{0,1\}^n\to\{0,1\}$ is famously characterized (via Yao's minimax) by the least number of queries needed to distinguish a distribution $D_0$ over $0$-inputs from a…
The generalization gap of a classifier is related to the complexity of the set of functions among which the classifier is chosen. We study a family of low-complexity classifiers consisting of thresholding a random one-dimensional feature.…
It is well known that ZFC, despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely many axioms, and it has a countable model due to the…
A Boolean function $f:\{0,1\}^n \to \{0,1\}$ is said to be noise sensitive if inserting a small random error in its argument makes the value of the function almost unpredictable. Benjamini, Kalai and Schramm showed that if the sum of…
Operations Research (OR) is vital for decision-making in many industries. While recent OR methods have seen significant improvements in automation and efficiency through integrating Large Language Models (LLMs), they still struggle to…
In the face of uncertainty, the need for probabilistic assessments has long been recognized in the literature on forecasting. In classification, however, comparative evaluation of classifiers often focuses on predictions specifying a single…
We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection $\{(S_i,l_i)\}_{i=1}^n$, where each $S_i$ is a sample drawn from the probability distribution of $X_i…
Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective, etc. Each such set is described by a single Set Theory formula with parameters unrelated to other formulas. Exotic expressions involving…
We completely characterise the complexity in the decision tree model of computing composite relations of the form h = g(f^1,...,f^n), where each relation f^i is boolean-valued. Immediate corollaries include a direct sum theorem for decision…
We study the model-checking problem for recursion schemes: does the tree generated by a given higher-order recursion scheme satisfy a given logical sentence. The problem is known to be decidable for sentences of the MSO logic. We prove…
Selective inference (post-selection inference) is a methodology that has attracted much attention in recent years in the fields of statistics and machine learning. Naive inference based on data that are also used for model selection tends…
Solomonoff sequence prediction is a scheme to predict digits of binary strings without knowing the underlying probability distribution. We call a prediction scheme informed when it knows the true probability distribution of the sequence.…