相关论文: On the number of relevant variables for discrete f…

We generalize and extend the ideas in a recent paper of Chiarelli, Hatami and Saks to prove new bounds on the number of relevant variables for boolean functions in terms of a variety of complexity measures. Our approach unifies and refines…

The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…

We study the number of real rational degree n functions (considered up to linear fractional transformations of the independent variable) with a given set of 2n-2 distinct real critical values. We present a combinatorial reformulation of…

This work explores the effects of relevant and irrelevant boolean variables on the accuracy of classifiers. The analysis uses the assumption that the variables are conditionally independent given the class, and focuses on a natural family…

A classical theorem of Nisan and Szegedy says that a boolean function with degree $d$ as a real polynomial depends on at most $d2^{d-1}$ of its variables. In recent work by Chiarelli, Hatami and Saks, this upper bound was improved to $C…

In this paper, some classes of discrete functions of $k$-valued logic are considered, that depend on sets of their variables in a particular way. Obtained results allow to "construct" these functions and to present them in their tabular,…

Boolean functions are important primitives in different domains of cryptology, complexity and coding theory. In this paper, we connect the tools from cryptology and complexity theory in the domain of Boolean functions with low polynomial…

The goal of the paper is to relate complexity measures associated with the evaluation of Boolean functions (certificate complexity, decision tree complexity) and learning dimensions used to characterize exact learning (teaching dimension,…

Boolean functions and their representation through logics, circuits, machine learning classifiers, or binary decision diagrams (BDDs) play a central role in the design and analysis of computing systems. Quantifying the relative impact of…

The sensitivity of a Boolean function f is the maximum over all inputs x, of the number of sensitive coordinates of x. The well-known sensitivity conjecture of Nisan (see also Nisan and Szegedy) states that every sensitivity-s Boolean…

Variable importance is central to scientific studies, including the social sciences and causal inference, healthcare, and other domains. However, current notions of variable importance are often tied to a specific predictive model. This is…

For a Boolean function $\Phi\colon\{0,1\}^d\to\{0,1\}$ and an assignment to its variables $\mathbf{x}=(x_1, x_2, \dots, x_d)$ we consider the problem of finding the subsets of the variables that are sufficient to determine the function…

We study the most-informative Boolean function conjecture using a differential equation approach. This leads to a formulation of a functional inequality on finite-dimensional random variables. We also develop a similar inequality in the…

Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…

Differential sensitivity measures provide valuable tools for interpreting complex computational models used in applications ranging from simulation to algorithmic prediction. Taking the derivative of the model output in direction of a model…

In biomedical research the use of discrete scales which describe characteristics of individuals are widely applied for the evaluation of clinical conditions. However, the number of classes (partitions) used in a discrete scale has never…

Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…

A Boolean function $f({\vec x})$ is sensitive to bit $x_i$ if there is at least one input vector $\vec x$ and one bit $x_i$ in $\vec x$, such that changing $x_i$ changes $f$. A function has sensitivity $s$ if among all input vectors, the…

A critical value of a function is the value of this function at one of its critical points. Each critical point of a differentiable multivariate function is described by the equations which consist in equating to zero all of its partial…

Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…