Related papers: Yay for Determinants!
Efficiently selecting indexes is fundamental to database performance optimization, particularly for systems handling large-scale analytical workloads. While deep reinforcement learning (DRL) has shown promise in automating index selection…
We explore the idea of using finite automata to implement new constraints for local search (this is already a successful technique in constraint-based global search). We show how it is possible to maintain incrementally the violations of a…
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
Explainable recommendation systems leverage transparent reasoning to foster user trust and improve decision-making processes. Current approaches typically decouple recommendation generation from explanation creation, violating causal…
We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training…
Forecasts support decision making in a variety of applications. Statistical models can produce accurate forecasts given abundant training data, but when data is sparse, rapidly changing, or unavailable, statistical models may not be able to…
Judgmental forecasting employs human opinions to make predictions about future events, rather than exclusively historical data as in quantitative forecasting. When these opinions form an argumentative structure around forecasts, it is…
Regression on observational data can fail to capture a causal relationship in the presence of unobserved confounding. Confounding strength measures this mismatch, but estimating it requires itself additional assumptions. A common assumption…
The problem is to determine which processors are reliable in a remote location by asking "Yes or No" questions. The processors are of three types: those that always tell the truth, those that always lie, and those the sometimes tell the…
Recovering causal structure in the presence of latent variables is an important but challenging task. While many methods have been proposed to handle it, most of them require strict and/or untestable assumptions on the causal structure. In…
Determinants of structured matrices play a fundamental role in both pure and applied mathematics, with wide-ranging applications in linear algebra, combinatorics, coding theory, and numerical analysis. In this work, the enumeration of…
We prove a formula which generalizes both Onn's colorful determinantal formula, related to Rota's basis conjecture, and Svrtan's $n!$ formula, related to the Atiyah-Sutcliffe problem. In some cases, our formula allows us to prove some…
We give a simple proof of a major index determinant formula in the symmetric group discovered by Krattenthaler and first proved by Thibon using noncommutative symmetric functions. We do so by proving a factorization of an element in the…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Conditor is a software tool which works with textual documents containing historical information. The purpose of this work two-fold: firstly to show the validity of the developed engine to correctly identify and label the entities of the…
We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…
Dodgson's method of computing determinants was recently revisited in a paper that appeared in the College Math Journal. The method is attractive, but fails if an interior entry of an intermediate matrix has the value zero. This paper…
Dickson's Lemma is a simple yet powerful tool widely used in termination proofs, especially when dealing with counters or related data structures. However, most computer scientists do not know how to derive complexity upper bounds from such…
We develop operators for construction of proposals in probabilistic programs, which we refer to as inference combinators. Inference combinators define a grammar over importance samplers that compose primitive operations such as application…
Local decision rules are commonly understood to be more explainable, due to the local nature of the patterns involved. With numerical optimization methods such as gradient boosting, ensembles of local decision rules can gain good predictive…