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We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…
Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…
The Smallest Grammar Problem -- the problem of finding the smallest context-free grammar that generates exactly one given sequence -- has never been successfully applied to grammatical inference. We investigate the reasons and propose an…
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…
We present a probabilistic modeling and inference framework for discriminative analysis dictionary learning under a weak supervision setting. Dictionary learning approaches have been widely used for tasks such as low-level signal denoising…
Generalization problems in languages with binders involve computing the most common structure between expressions while respecting bound variable renaming and freshness constraints. These problems often lack a least general solution.…
Given only observational data $X = g(Z)$, where both the latent variables $Z$ and the generating process $g$ are unknown, recovering $Z$ is ill-posed without additional assumptions. Existing methods often assume linearity or rely on…
In this paper we are interested in the problem of learning an over-complete basis and a methodology such that the reconstruction or inverse problem does not need optimization. We analyze the optimality of the presented approaches, their…
We equip a smaller Language Model to generalise to answering challenging compositional questions that have not been seen in training. To do so we propose a combination of multitask supervised pretraining on up to 93 tasks designed to…
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…
In this paper, we investigate the principle that `good explanations are hard to vary' in the context of deep learning. We show that averaging gradients across examples -- akin to a logical OR of patterns -- can favor memorization and…
With the rapid development of information technologies, centralized data processing is subject to many limitations, such as computational overheads, communication delays, and data privacy leakage. Decentralized data processing over…
Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…
In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $\mathbb{R}^d$), and the goal is to find a "basis" in which the signals have a sparse (approximate) representation. The problem has…
Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict…
Meta-learning synthesizes and leverages the knowledge from a given set of tasks to rapidly learn new tasks using very little data. Meta-learning of linear regression tasks, where the regressors lie in a low-dimensional subspace, is an…
This paper investigates the theoretical guarantees of L1-analysis regularization when solving linear inverse problems. Most of previous works in the literature have mainly focused on the sparse synthesis prior where the sparsity is measured…
In this paper, we study the problem of recovering two unknown signals from their convolution, which is commonly referred to as blind deconvolution. Reformulation of blind deconvolution as a low-rank recovery problem has led to multiple…
In the present paper we consider application of overcomplete dictionaries to solution of general ill-posed linear inverse problems. Construction of an adaptive optimal solution for such problems usually relies either on a singular value…