New method combines domain changes and sparse mixing for better latent variable learning.
problem Challenges in identifying latent variables due to insufficient domain changes and violated sparsity constraints.
method Combines sufficient changes and sparse mixing constraints, using domain encoding networks and variational autoencoders.
result Identifiability of latent variables achieved with less restrictive constraints.
Paper tackles NAS problem by modeling it as a sparse supernet.
problem Neural Architecture Search (NAS) problem, particularly Mixed-Path Search.
method Model NAS as a sparse supernet with sparsity constraints. Use hierarchical accelerated proximal gradient algorithm for optimization.
result Proposed method finds compact, general, and powerful neural architectures.
New insights into statistical and computational limits for mixed sparse linear regression.
problem Recovering two sparse signals from noisy linear measurements.
method Analysis of low-degree polynomials and a simple thresholding algorithm.
result Identification of a smooth information-computation tradeoff and order-optimality of the thresholding algorithm.
Mixed membership factorization is a popular approach for analyzing data sets that have within-sample heterogeneity. In recent years, several algorithms have been developed for mixed membership matrix factorization, but they only guarantee estimates from a local optimum. Here, we derive a global optimization (GOP) algor…
This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a…
New RL method MAC improves performance in sparse reward settings.
problem Slow mixing in large state spaces or sparse rewards.
method Multi-level Monte Carlo Actor-Critic (MAC) algorithm.
result Achieves convergence rate comparable to state-of-the-art AC algorithms.
Bayesian method predicts runtime metrics for fog manufacturing.
problem Accurate prediction of runtime performance metrics in fog manufacturing.
method Bayesian sparse regression for multivariate mixed responses.
result Enhanced prediction and statistical inferences of runtime metrics.
Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods where feature selection is effected via mixed-norms. Several mixed-norm based spar…
Study on sparse recovery with mixed-quality data, establishing sample-size conditions.
problem Sparse recovery with heterogeneous noise from high- and low-quality sources.
method Establishes linear trade-off for sufficient conditions, analyzes LASSO algorithm.
result Linear trade-off for sufficient conditions, robustness of LASSO to data heterogeneity.
Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from all tasks. Therefore sparse solutions, that avoid using the entire data directly a…
Zero-inflated datasets, which have an excess of zero outputs, are commonly encountered in problems such as climate or rare event modelling. Conventional machine learning approaches tend to overestimate the non-zeros leading to poor performance. We propose a novel model family of zero-inflated Gaussian processes (ZiGP) …
We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal analysis and sparse learning proble…
Linear Mixed Models (LMMs) are important tools in statistical genetics. When used for feature selection, they allow to find a sparse set of genetic traits that best predict a continuous phenotype of interest, while simultaneously correcting for various confounding factors such as age, ethnicity and population structure…
Proposes a convex model for mixed logit to handle individual heterogeneity.
problem Non-convex optimization in mixed logit models for individual heterogeneity.
method Sparse and low-rank decomposition for convex formulation.
result Convex formulation avoids simulation-based approximation and unstable model interpretation.
The paper gives a constructive method, based on greedy algorithms, that provides for the classes of functions with small mixed smoothness the best possible in the sense of order approximation error for the m-term approximation with respect to the trigonometric system.
Paper uses machine learning for nowcasting corporate earnings from mixed-frequency data.
problem Predicting corporate earnings for a large cross-section of firms with different frequency data.
method Structured machine learning regressions with sparse-group LASSO regularization for panel data.
result Machine learning models outperform traditional methods in nowcasting corporate earnings.
Paper solves NP-hard sparse mixed linear regression problem with provable guarantees.
problem Sparse mixed linear regression on unlabeled data.
method Invex relaxation for intractable problem with theoretical guarantees.
result Exact recovery of data labels and close approximation of regression parameters.
The paper tackles deep learning from dependent data, achieving optimal performance.
problem Deep learning from strongly mixing observations, especially with regularization and optimality.
method Sparse-penalized regularization for deep neural networks, oracle inequality for expected excess risk.
result Deep neural network estimator achieves minimax optimal rate for nonparametric autoregression.
The paper improves machine learning for heavy-tailed panel data.
problem Improving estimates for financial and economic data with fat tails.
method Sparse-group LASSO regularization and Fuk-Nagaev concentration inequality.
result Oracle inequalities for panel data estimators.
This paper investigates the problem of sparse signal recovery in the presence of additive impulsive noise. The heavytailed impulsive noise is well modelled with stable distributions. Since there is no explicit formulation for the probability density function of SαS distribution, alternative approximations like Genera…
New method selects sparse predictors in large LMMs.
problem Sparse learning for LMMs is computationally infeasible for large datasets.
method Developed an ℓ0 regularized method with coordinate descent and local search algorithms. result Method selects thousands of predictors in seconds to minutes.
Paper proves EM algorithm convergence for mixtures of discrete and continuous parameters.
problem Nontrivial convergence analysis for EM algorithms with mixed-integer parameters.
method Introduces conditions for EM convergence in mixed-integer optimization.
result Proves convergence of EM-based sparse Bayesian learning algorithm.
Deep Belief Networks (DBN) have been successfully applied on popular machine learning tasks. Specifically, when applied on hand-written digit recognition, DBNs have achieved approximate accuracy rates of 98.8%. In an effort to optimize the data representation achieved by the DBN and maximize their descriptive power, re…
There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study oracle properties of LASSO estimation of weakly sparse vector-autoregressive model…
The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when the model is sparse, in that there is only a small amount of information availab…
Blind Source Separation is a widely used technique to analyze multichannel data. In many real-world applications, its results can be significantly hampered by the presence of unknown outliers. In this paper, a novel algorithm coined rGMCA (robust Generalized Morphological Component Analysis) is introduced to retrieve s…
New method estimates causal structure from sparse data.
problem Inferring causal structure from sparse observational data.
method Log-likelihood of sparsely mixed ICA with penalty terms.
result Proposed method outperforms existing methods.
This work tackles sparse coding in DLRA for interpretable multiway data.
problem Sparse coding in DLRA for interpretable multiway data.
method Proposes a new sparse-coding subproblem (MSC) and several algorithms to solve it.
result DLRA extends low-rank approximations, reducing variance and enhancing interpretability.
Proposes a boosting framework for sparsity in grouped covariates.
problem Sparsity and selection bias in grouped covariates.
method Component-wise and group-wise gradient boosting with adjusted degrees of freedom.
result Reduces bias and improves predictability in variable selection.
New method optimizes mixed integer optimization for hierarchical modeling of clustered and longitudinal data.
problem Optimizing subset selection in hierarchical models with clustered and longitudinal data.
method Distribution-free mixed-integer optimization approach for cluster-aware regression.
result The method efficiently solves problems within minutes and outperforms traditional models in generating sparse solutions with high predictive power.
Improved Compressed Sensing by optimizing sparse solutions with mixed integer programming.
problem Finding sparse solutions to linear measurements with numerical tolerance.
method Introducing an ℓ2 regularized formulation, reformulating as a mixed integer second order cone program, deriving a second order cone relaxation, and developing a custom branch-and-bound algorithm. result Our approach produces solutions that are on average 6.22% more sparse compared to state-of-the-art methods.
Efficient algorithms recover two sparse models from a mix of linear queries.
problem Recovering two sparse models from a mix of linear queries.
method Efficient algorithms for query complexity problem.
result Improved query complexity for model recovery.
New model captures insurance risk dependencies efficiently.
problem Dependence modeling in sparse time series of insurance claims.
method Comb-Bernoulli model bridging Lévy copulas and zero-mixed models.
result Model enables tractable simulation, likelihood evaluation, and parameter estimation.
Paper introduces DP methods for high-dimensional variable selection.
problem Sparse variable selection in high-dimensional learning.
method Pure differentially private estimators using Integer Programming.
result Achieves state-of-the-art empirical support recovery.
New MIP approach for efficient change-point detection.
problem Offline multiple change-point detection in data streams.
method Mixed-integer programming (MIP) for globally optimal PWL fitting.
result Provable tighter relaxations for segment assignment variables.
This paper proposes exact and approximation algorithms for Sparse PCA, improving interpretability and scalability.
problem Selecting a prespecified-size principal submatrix from a covariance matrix to maximize its largest eigenvalue.
method Proposes two exact mixed-integer SDPs and a mixed-integer linear program (MILP) for SPCA, analyzes theoretical optimality gaps, and develops approximation algorithms.
result The proposed algorithms achieve strong theoretical optimality and effective scalability, with continuous relaxations close to optimality and MILP solving small to medium-size instances.
Develops a deep learning framework for various data types.
problem Handling nonparametric regression and classification across different data types.
method Introduces a general framework with two estimators: NPDNN and SPDNN, based on data satisfying generalized Bernstein-type inequalities.
result Both NPDNN and SPDNN estimators are minimax optimal in many classical settings.
Sparse-penalized deep neural networks improve performance in weakly dependent processes.
problem Nonparametric regression and classification under weak dependence.
method Sparse-penalized deep neural networks with oracle inequalities and convergence rates established.
result The proposed estimators outperform non-penalized ones in simulations.
DCRL learns causal relationships from mixed-type discrete data.
problem Challenges in learning causal relationships from discrete, mixed-type data.
method Generative framework modeling directed acyclic graph and sparse bipartite graph, flexible measurement models for different types of data.
result Consistent recovery of latent causal structure from observed data distribution.
New sparse penalty improves biclustering for gene expression data.
problem Identifying significant clusters in gene expression data.
method Prenet penalty applied to SSVD for biclustering.
result Mixed Prenet penalty effectively clusters non-overlapped data.
Inductive Matrix Completion (IMC) is an important class of matrix completion problems that allows direct inclusion of available features to enhance estimation capabilities. These models have found applications in personalized recommendation systems, multilabel learning, dictionary learning, etc. This paper examines a g…
Non-negative curvature affects Markov chains' mixing and expansion properties.
problem Understanding the behavior of Markov chains with non-negative curvature.
method Analyzing conductance, displacement, and cutoff phenomenon in sparse Markov chains.
result Non-negatively curved Markov chains exhibit specific, non-standard behavior in terms of mixing and expansion.
A DP method selects best sparse models in high dimensions efficiently.
problem Model selection in high-dimensional sparse linear regression under privacy constraints.
method Differential privacy (DP) with exponential mechanism and Metropolis-Hastings algorithm.
result The method identifies active features quickly under privacy constraints.
Study on recovering supports of multiple sparse vectors from mixed linear measurements.
problem Recovering supports of multiple sparse vectors from a mixture of linear measurements.
method Developed algorithms to identify the support of all component vectors using polynomial and quasi-polynomial number of measurements.
result Polynomial and quasi-polynomial number of measurements sufficient for recovering the supports of all component vectors.
A universal framework for constructing confidence sets using sequential likelihood mixing.
problem Constructing reliable confidence sets for realizable likelihood functions.
method Sequential likelihood mixing, integrating Bayesian inference and regret inequalities.
result Establishes fundamental connections and provable coverage guarantees for various inference techniques.
We propose a nonparametric method for detecting nonlinear causal relationship within a set of multidimensional discrete time series, by using sparse additive models (SpAMs). We show that, when the input to the SpAM is a β-mixing time series, the model can be fitted by first approximating each unknown function with a …
Convolutional neural network (CNN) and its variants have led to many state-of-art results in various fields. However, a clear theoretical understanding about them is still lacking. Recently, multi-layer convolutional sparse coding (ML-CSC) has been proposed and proved to equal such simply stacked networks (plain networ…
We derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects. In the most general situation, where the dimensions of the crossed groups are arbitrarily large, streamlining is hindered by lack of sparseness in the underlying least squares system. Because of th…