Related papers: Information in propositional proofs and algorithmi…
The simplicial condition and other stronger conditions that imply it have recently played a central role in developing polynomial time algorithms with provable asymptotic consistency and sample complexity guarantees for topic estimation in…
This paper studies privacy in the context of complex decision support queries composed of multiple conditions on different aggregate statistics combined using disjunction and conjunction operators. Utility requirements for such queries…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
We give upper and lower bounds on the power of subsystems of the Ideal Proof System (IPS), the algebraic proof system recently proposed by Grochow and Pitassi, where the circuits comprising the proof come from various restricted algebraic…
Robust learning in expressive languages with real-world data continues to be a challenging task. Numerous conventional methods appeal to heuristics without any assurances of robustness. While probably approximately correct (PAC) Semantics…
In the SEARCH WITH ADVICE problem, a single entry of interest within a database of N entries is to be found assuming that an ordering of the entries, from that with the highest probability of being the entry of interest (as determined by a…
Advances in the effectiveness of machine learning models have come at the cost of enormous complexity resulting in a poor understanding of how they function. Local surrogate methods have been used to approximate the workings of these…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
We study ordinal approximation algorithms for maximum-weight bipartite matchings. Such algorithms only know the ordinal preferences of the agents/nodes in the graph for their preferred matches, but must compete with fully omniscient…
Reinforcement learning (RL) aims to find an optimal policy by interaction with an environment. Consequently, learning complex behavior requires a vast number of samples, which can be prohibitive in practice. Nevertheless, instead of…
This paper presents a new foundational approach to information theory based on the concept of the information efficiency of a recursive function, which is defined as the difference between the information in the input and the output. The…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
We provide the first evidence for the inherent difficulty of finding complex sets with optimal proof systems. For this, we construct oracles $O_1$ and $O_2$ with the following properties, where $\mathrm{RE}$ denotes the class of recursively…
We introduce a novel framework for analyzing sorting algorithms in pairwise ranking prompting (PRP), re-centering the cost model around LLM inferences rather than traditional pairwise comparisons. While classical metrics based on comparison…
Estimating causal interactions in complex dynamical systems is an important problem encountered in many fields of current science. While a theoretical solution for detecting the causal interactions has been previously formulated in the…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
We propose a general methodology for testing whether a given polynomial with integer coefficients is identically zero. The methodology evaluates the polynomial at efficiently computable approximations of suitable irrational points. In…
When additional information sources are available in decision making problems that allow stochastic optimization formulations, an important question is how to optimally use the information the sources are capable of providing. A framework…
It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras…