Related papers: Analyzing Multifiltering Functions Using Multipara…

We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large size. Based on a common graph-based formalism, we analyze existing data structures for simplicial…

Mathematical morphology (MM) helps to describe and analyze shapes using set theory. MM can be effectively applied to binary images which are treated as sets. Basic morphological operators defined can be used as an effective tool in image…

The Poisson multi-Bernoulli mixture (PMBM) filter is conjugate prior composed of the union of a Poisson point process (PPP) and a multi-Bernoulli mixture (MBM). In this paper, a new PMBM filter for tracking multiple targets with randomly…

Embedding based models have been the state of the art in collaborative filtering for over a decade. Traditionally, the dot product or higher order equivalents have been used to combine two or more embeddings, e.g., most notably in matrix…

Bloom filters are widely used data structures that compactly represent sets of elements. Querying a Bloom filter reveals if an element is not included in the underlying set or is included with a certain error rate. This membership testing…

The survey is devoted to the combinatorial and metric theory of filtrations, i.\,e., decreasing sequences of $\sigma$-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras. One of the key notions, that of…

Continuing our recent work we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider such polynomial masks that are derived by means of the…

We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which allow a separation into frequency-band components, one for each of the ranges of bands, say…

Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…

Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition. We extend these models to the multi-output setting, i.e., for learning vector-valued functions, with application…

Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep…

High-dimensional datasets depict a challenge for learning tasks in data mining and machine learning. Feature selection is an effective technique in dealing with dimensionality reduction. It is often an essential data processing step prior…

Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior…

We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…

In this paper we develope a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known Morsification results for non-isolated singulatities and…

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…

Many multi-object estimation problems require additional estimation of model or sensor parameters that are either common to all objects or related to unknown characterisation of one or more sensors. Important examples of these include…

Density functional theory (DFT), the most widely adopted method in modern computational chemistry, fails to describe accurately the electronic structure of strongly correlated systems. Here we show that DFT can be formally and practically…

The Poisson Multi-Bernoulli Mixture (PMBM) density is a conjugate multi-target density for the standard point target model with Poisson point process birth. This means that both the filtering and predicted densities for the set of targets…

Collaborative filtering is one of the most popular techniques in designing recommendation systems, and its most representative model, matrix factorization, has been wildly used by researchers and the industry. However, this model suffers…