Related papers: Measure Recognition Problem

We study the dynamics of polynomial-like mappings in several variables. A special case of our results is the following theorem. Let f be a proper holomorphic map from an open set U onto a Stein manifold V, $U\subset\subset V$. Assume f is…

We will study some important properties of Boolean functions based on newly introduced concepts called Special Decomposition of a Set and Special Covering of a Set. These concepts enable us to study important problems concerning Boolean…

In multi-label learning, each instance is associated with multiple labels and the crucial task is how to leverage label correlations in building models. Deep neural network methods usually jointly embed the feature and label information…

We develop a mathematical framework to address a broad class of metric and preference learning problems within a Hilbert space. We obtain a novel representer theorem for the simultaneous task of metric and preference learning. Our key…

Partial Multi-label Learning (PML) is a type of weakly supervised learning where each training instance corresponds to a set of candidate labels, among which only some are true. In this paper, we introduce \our{}, a novel probabilistic…

A key element of any machine learning algorithm is the use of a function that measures the dis/similarity between data points. Given a task, such a function can be optimized with a metric learning algorithm. Although this research field has…

Inspired by long-standing open problems in algebraic combinatorics, we show that modern machine learning can meaningfully contribute to verifiable mathematical discoveries. In particular, we focus on the construction of simple mathematical…

Prediction of material property is a key problem because of its significance to material design and screening. We present a brand-new and general machine learning method for material property prediction. As a representative example, polymer…

Distance metric learning is of fundamental interest in machine learning because the distance metric employed can significantly affect the performance of many learning methods. Quadratic Mahalanobis metric learning is a popular approach to…

This paper studies recurrence phenomena in iterative holomorphic dynamics of certain multi-valued maps. In particular, we prove an analogue of the Poincar\'e recurrence theorem for meromorphic correspondences with respect to certain…

Most existing metric learning methods focus on learning a similarity or distance measure relying on similar and dissimilar relations between sample pairs. However, pairs of samples cannot be simply identified as similar or dissimilar in…

In "Unlabeled Sensing", one observes a set of linear measurements of an underlying signal with incomplete or missing information about their ordering, which can be modeled in terms of an unknown permutation. Previous work on the case of a…

Metric Ramsey theory is concerned with finding large well-structured subsets of more complex metric spaces. For finite metric spaces this problem was first studies by Bourgain, Figiel and Milman \cite{bfm}, and studied further in depth by…

We propose a new approach to combine Restricted Boltzmann Machines (RBMs) that can be used to solve combinatorial optimization problems. This allows synthesis of larger models from smaller RBMs that have been pretrained, thus effectively…

A Boolean $\sigma$-algebra $B$ is a measure algebra if and only if it is weakly distributive and uniformly concentrated.

The analysis of mixed data has been raising challenges in statistics and machine learning. One of two most prominent challenges is to develop new statistical techniques and methodologies to effectively handle mixed data by making the data…

Set-membership estimation is usually formulated in the context of set-valued calculus and no probabilistic calculations are necessary. In this paper, we show that set-membership estimation can be equivalently formulated in the probabilistic…

We (claim to) prove the extremely surprising fact that NP=RP. It is achieved by creating a Fully Polynomial-Time Randomized Approximation Scheme (FPRAS) for approximately counting the number of independent sets in bounded degree graphs,…

Metric learning seeks a transformation of the feature space that enhances prediction quality for the given task at hand. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lower- and…

Combinatorial discrepancy is a complexity measure of a collection of sets which quantifies how well the sets in the collection can be simultaneously balanced. More precisely, we are given an n-point set $P$, and a collection $\mathcal{F} =…