Related papers: Performance Limits of Dictionary Learning for Spar…
In this paper, we investigate the problem of optimization multivariate performance measures, and propose a novel algorithm for it. Different from traditional machine learning methods which optimize simple loss functions to learn prediction…
Dictionary learning aims to find a dictionary that can sparsely represent the training data. Methods in the literature typically formulate the dictionary learning problem as an optimisation with respect to two variables, i.e., dictionary…
In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies,…
Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix…
We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast…
We consider a learning problem of identifying a dictionary matrix D (M times N dimension) from a sample set of M dimensional vectors Y = N^{-1/2} DX, where X is a sparse matrix (N times P dimension) in which the density of non-zero entries…
This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing…
Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse…
Sparse representations using learned dictionaries are being increasingly used with success in several data processing and machine learning applications. The availability of abundant training data necessitates the development of efficient,…
Dictionary learning consists of finding a sparse representation from noisy data and is a common way to encode data-driven prior knowledge on signals. Alternating minimization (AM) is standard for the underlying optimization, where gradient…
Deep learning has been applied to various tasks in the field of machine learning and has shown superiority to other common procedures such as kernel methods. To provide a better theoretical understanding of the reasons for its success, we…
Recently, machine learning-based channel estimation has attracted much attention. The performance of machine learning-based estimation has been validated by simulation experiments. However, little attention has been paid to the theoretical…
Sparse dictionary learning is a popular method for representing signals as linear combinations of a few elements from a dictionary that is learned from the data. In the classical setting, signals are represented as vectors and the…
Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these models…
In this paper, we address the problem of discriminative dictionary learning (DDL), where sparse linear representation and classification are combined in a probabilistic framework. As such, a single discriminative dictionary and linear…
We propose and analyze a novel framework for learning sparse representations, based on two statistical techniques: kernel smoothing and marginal regression. The proposed approach provides a flexible framework for incorporating feature…
The efficient sparse coding and reconstruction of signal vectors via linear observations has received a tremendous amount of attention over the last decade. In this context, the automated learning of a suitable basis or overcomplete…
Dictionary learning aims at seeking a dictionary under which the training data can be sparsely represented. Methods in the literature typically formulate the dictionary learning problem as an optimization w.r.t. two variables, i.e.,…
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…
Sparse representation over redundant dictionaries constitutes a good model for many classes of signals (e.g., patches of natural images, segments of speech signals, etc.). However, despite its popularity, very little is known about the…