Related papers: On some deterministic dictionaries supporting spar…
Vacillating tableaux are sequences of integer partitions that satisfy specific conditions. The concept of vacillating tableaux stems from the representation theory of the partition algebra and the combinatorial theory of crossings and…
Dictionaries are collections of vectors used for representations of elements in Euclidean spaces. While recent research on optimal dictionaries is focussed on providing sparse (i.e., $\ell_0$-optimal,) representations, here we consider the…
We consider the problem of aggregating the elements of a possibly infinite dictionary for building a decision procedure that aims at minimizing a given criterion. Along with the dictionary, an independent identically distributed training…
In an effort to better understand meaning from natural language texts, we explore methods aimed at organizing lexical objects into contexts. A number of these methods for organization fall into a family defined by word ordering. Unlike…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
It is possible to construct representations of the Lorentz group using four-dimensional harmonic oscillators. This allows us to construct three-dimensional wave functions with the usual rotational symmetry for space-like coordinates and…
Structured sparse coding and the related structured dictionary learning problems are novel research areas in machine learning. In this paper we present a new application of structured dictionary learning for collaborative filtering based…
A vocabulary is a list of words designating subsets from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is…
Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…
In this paper, we propose and investigate algorithms for the structured orthogonal dictionary learning problem. First, we investigate the case when the dictionary is a Householder matrix. We give sample complexity results and show…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$. This is a central notion in signal processing, statistics and machine learning. But in…
Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can…
For every odd prime $p$ and every integer $n\geq 12$ there is a Heisenberg group of order $p^{5n/4+O(1)}$ that has $p^{n^2/24+O(n)}$ pairwise nonisomorphic quotients of order $p^{n}$. Yet, these quotients are virtually indistinguishable.…
We consider indecomposable representations of the Klein four group over a field of characteristic $2$ and of a cyclic group of order $pm$ with $p,m$ coprime over a field of characteristic $p$. For each representation we explicitly describe…
A choice dictionary is a data structure that can be initialized with a parameter $n\in\{1,2,\ldots\}$ and subsequently maintains an initially empty subset $S$ of $\{1,\ldots,n\}$ under insertion, deletion, membership queries and an…
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
The aim of this paper is to introduce a novel dictionary learning algorithm for sparse representation of signals defined over combinatorial topological spaces, specifically, regular cell complexes. Leveraging Hodge theory, we embed topology…
To an orthogonal or unitary involution on a central simple algebra of degree 4, or to a symplectic involution on a central simple algebra of degree 8, we associate a Pfister form that characterises the decomposability of the algebra with…
Recent work on vector-based compositional natural language semantics has proposed the use of density matrices to model lexical ambiguity and (graded) entailment (e.g. Piedeleu et al 2015, Bankova et al 2019, Sadrzadeh et al 2018). Ambiguous…