Related papers: The Optimal Arbitrary-Proportional Finite-Set-Part…
We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…
In this paper, we solve a maximization problem where the objective function is quadratic and convex or concave and the constraints set is the reachable value set of a convergent discrete-time affine system. Moreover, we assume that the…
The classical Busemann-Petty problem asks whether smaller central hyperplane sections of origin-symmetric convex bodies necessarily imply smaller total volume. Zvavitch studied this question for arbitrary measures with continuous even…
We consider the classical minimum and maximum cut problems: find a partition of vertices of a graph into two disjoint subsets that minimize or maximize the sum of the weights of edges with endpoints in different subsets. It is known that if…
We propose a new approach for solving a class of discrete decision making problems under uncertainty with positive cost. This issue concerns multiple and diverse fields such as engineering, economics, artificial intelligence, cognitive…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
Diversity plays a crucial role in multiple contexts such as team formation, representation of minority groups and generally when allocating resources fairly. Given a community composed by individuals of different types, we study the problem…
Conformal prediction is a generic methodology for finite-sample valid distribution-free prediction. This technique has garnered a lot of attention in the literature partly because it can be applied with any machine learning algorithm that…
We consider the problem of estimating the missing mass, partition function or evidence and its probability distribution in the case that for each sample point in the discrete sample space its (unnormalized) probability mass is revealed.…
In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…
The main purpose of Feature Subset Selection is to find a reduced subset of attributes from a data set described by a feature set. The task of a feature selection algorithm (FSA) is to provide with a computational solution motivated by a…
We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that the errors…
Cost-and-Quality (CQ) controllability in arbitrary-scale super-resolution is crucial. Existing methods predict Fourier components one by one using a recurrent neural network. However, this approach leads to performance degradation and…
We formalize a new paradigm for optimality of algorithms, that generalizes worst-case optimality based only on input-size to problem-dependent parameters including implicit ones. We re-visit some existing sorting algorithms from this…
We pursue the question how integers can be ordered or partitioned according to their divisibility properties. Based on pseudometrics on $\mathbb{Z}$, we investigate induced preorders, associated equivalence relations, and quotient sets. The…
We consider the following generalization of the bin packing problem. We are given a set of items each of which is associated with a rational size in the interval [0,1], and a monotone non-decreasing non-negative cost function f defined over…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…