Related papers: Oblivious Bounds on the Probability of Boolean Fun…

This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…

Let $\mathsf{TH}_k$ denote the $k$-out-of-$n$ threshold function: given $n$ input Boolean variables, the output is $1$ if and only if at least $k$ of the inputs are $1$. We consider the problem of computing the $\mathsf{TH}_k$ function…

In Bayesian Optimization (BO), additive assumptions can mitigate the twin difficulties of modeling and searching a complex function in high dimension. However, common acquisition functions, like the Additive Lower Confidence Bound, ignore…

For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…

We are often interested in identifying the feasible subset of a decision space under multiple constraints to permit effective design exploration. If determining feasibility required computationally expensive simulations, the cost of…

Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of…

As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…

Pairwise learning focuses on learning tasks with pairwise loss functions, depends on pairs of training instances, and naturally fits for modeling relationships between pairs of samples. In this paper, we focus on the privacy of pairwise…

We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state…

Motivated by the poor performance of cross-validation in settings where data are scarce, we propose a novel estimator of the out-of-sample performance of a policy in data-driven optimization.Our approach exploits the optimization problem's…

Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…

A central computational problem for analyzing and model checking various classes of infinite-state recursive probabilistic systems (including quasi-birth-death processes, multi-type branching processes, stochastic context-free grammars,…

The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…

Boolean functions and networks are commonly used in the modeling and analysis of complex biological systems, and this paradigm is highly relevant in other important areas in data science and decision making, such as in the medical field and…

We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by…

We derive two related novel bounds on single-variable marginal probability distributions in factor graphs with discrete variables. The first method propagates bounds over a subtree of the factor graph rooted in the variable, and the second…

Data separation is a well-studied phenomenon that can cause problems in the estimation and inference from binary response models. Complete or quasi-complete separation occurs when there is a combination of regressors in the model whose…

Probabilities of causation (PoCs) are fundamental quantities for counterfactual analysis and personalized decision making. However, existing analytical results are largely confined to binary settings. This paper extends PoCs to multi-valued…

Nisan and Szegedy (CC 1994) showed that any Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ that depends on all its input variables, when represented as a real-valued multivariate polynomial $P(x_1,\ldots,x_n)$, has degree at least $\log…

The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…