相关论文: Optimal estimation of sparse topic models

This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…

We consider support recovery in the quadratic logistic regression setting - where the target depends on both p linear terms $x_i$ and up to $p^2$ quadratic terms $x_i x_j$. Quadratic terms enable prediction/modeling of higher-order effects…

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

Traditional topic models are effective at uncovering latent themes in large text collections. However, due to their reliance on bag-of-words representations, they struggle to capture semantically abstract features. While some neural…

We consider the problem of dictionary learning under the assumption that the observed signals can be represented as sparse linear combinations of the columns of a single large dictionary matrix. In particular, we analyze the minimax risk of…

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

Recently, Neural Topic Models (NTMs) inspired by variational autoencoders have obtained increasingly research interest due to their promising results on text analysis. However, it is usually hard for existing NTMs to achieve good document…

We present a token-level decision summarization framework that utilizes the latent topic structures of utterances to identify "summary-worthy" words. Concretely, a series of unsupervised topic models is explored and experimental results…

Many real-world data sets are sparse or almost sparse. One method to measure this for a matrix $A\in \mathbb{R}^{n\times n}$ is the \emph{numerical sparsity}, denoted $\mathsf{ns}(A)$, defined as the minimum $k\geq 1$ such that…

In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its…

Inferring topics from the overwhelming amount of short texts becomes a critical but challenging task for many content analysis tasks, such as content charactering, user interest profiling, and emerging topic detecting. Existing methods such…

Topic models are in widespread use in natural language processing and beyond. Here, we propose a new framework for the evaluation of probabilistic topic modeling algorithms based on synthetic corpora containing an unambiguously defined…

Approximate inference via information projection has been recently introduced as a general-purpose approach for efficient probabilistic inference given sparse variables. This manuscript goes beyond classical sparsity by proposing efficient…

We analyze the decomposition of a data matrix, assumed to be a superposition of a low-rank component and a component which is sparse in a known dictionary, using a convex demixing method. We provide a unified analysis, encompassing both…

Statistical topic models provide a general data-driven framework for automated discovery of high-level knowledge from large collections of text documents. While topic models can potentially discover a broad range of themes in a data set,…

We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in…

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…

In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit…