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A key aspect of machine learning models lies in their ability to learn efficient intermediate features. However, the input representation plays a crucial role in this process, and polyphonic musical scores remain a particularly complex type…

In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We…

Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We…

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…

An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can…

In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…

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…

Recent work has demonstrated that using a carefully designed dictionary instead of a predefined one, can improve the sparsity in jointly representing a class of signals. This has motivated the derivation of learning methods for designing a…

We consider the problem of distributed dictionary learning, where a set of nodes is required to collectively learn a common dictionary from noisy measurements. This approach may be useful in several contexts including sensor networks.…

We describe new results and algorithms for two different, but related, problems which deal with circulant matrices: learning shift-invariant components from training data and calculating the shift (or alignment) between two given signals.…

Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As…

Words can have multiple senses. Compositional distributional models of meaning have been argued to deal well with finer shades of meaning variation known as polysemy, but are not so well equipped to handle word senses that are…

The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…

In this paper, we develop a parameter estimation method for factorially parametrized models such as Factorial Gaussian Mixture Model and Factorial Hidden Markov Model. Our contributions are two-fold. First, we show that the emission matrix…

Dictionary learning is a popular approach for inferring a hidden basis or dictionary in which data has a sparse representation. Data generated from the dictionary A (an n by m matrix, with m > n in the over-complete setting) is given by Y =…

We explore a novel way of conceptualising the task of polyphonic music transcription, using so-called invertible neural networks. Invertible models unify both discriminative and generative aspects in one function, sharing one set of…

A dictionary is a database of standard vectors, so that other vectors / signals are expressed as linear combinations of dictionary vectors, and the task of learning a dictionary for a given data is to find a good dictionary so that the…

Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or…

We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rank-reducing term similar to the trace norm. In…

Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular…