Related papers: Structured model selection via $\ell_1-\ell_2$ opt…
In order to optimally design materials, it is crucial to understand the structure-property relations in the material by analyzing the effect of microstructure parameters on the macroscopic properties. In computational homogenization, the…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
We study a theoretical and algorithmic framework for structured prediction in the online learning setting. The problem of structured prediction, i.e. estimating function where the output space lacks a vectorial structure, is well studied in…
Augmenting a smooth cost function with an $\ell_1$ penalty allows analysts to efficiently conduct estimation and variable selection simultaneously in sophisticated models and can be efficiently implemented using proximal gradient methods.…
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…
A multi-scale approach to the inverse reconstruction of a pattern's microstructure is reported. Instead of a correlation function, a pair of entropic descriptors (EDs) is proposed for stochastic optimization method. The first of them…
In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse…
The problem of feature selection has raised considerable interests in the past decade. Traditional unsupervised methods select the features which can faithfully preserve the intrinsic structures of data, where the intrinsic structures are…
Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
Decision-making in complex systems often relies on machine learning models, yet highly accurate models such as XGBoost and neural networks can obscure the reasoning behind their predictions. In operations research applications,…
We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…
We develop a new framework for learning variational autoencoders and other deep generative models that balances generative and discriminative goals. Our framework optimizes model parameters to maximize a variational lower bound on the…
Modeling dynamical systems and unraveling their underlying causal relationships is central to many domains in the natural sciences. Various physical systems, such as those arising in cell biology, are inherently high-dimensional and…
Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…
In this paper we introduce a nonuniform sparsity model and analyze the performance of an optimized weighted $\ell_1$ minimization over that sparsity model. In particular, we focus on a model where the entries of the unknown vector fall into…
We consider linear models for stochastic dynamics. To any such model can be associated a network (namely a directed graph) describing which degrees of freedom interact under the dynamics. We tackle the problem of learning such a network…
We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal…
Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…