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Found 11 papers, 3 papers with code
Estimation and inference for the Wasserstein distance between mixing measures in topic models
Our results establish this metric to be a canonical choice.
Likelihood estimation of sparse topic distributions in topic models and its applications to Wasserstein document distance calculations
When $A$ is unknown, we estimate $T$ by optimizing the likelihood function corresponding to a plug in, generic, estimator $\hat{A}$ of $A$.
Prediction in latent factor regression: Adaptive PCR and beyond
Our primary contribution is in establishing finite sample risk bounds for prediction with the ubiquitous Principal Component Regression (PCR) method, under the factor regression model, with the number of principal components adaptively selected from the data -- a form of theoretical guarantee that is surprisingly lacking from the PCR literature.
Interpolating Predictors in High-Dimensional Factor Regression
If the effective rank of the covariance matrix $\Sigma$ of the $p$ regression features is much larger than the sample size $n$, we show that the min-norm interpolating predictor is not desirable, as its risk approaches the risk of trivially predicting the response by 0.
Optimal estimation of sparse topic models
We derive a finite sample upper bound for our estimator, and show that it matches the minimax lower bound in many scenarios.
High-Dimensional Inference for Cluster-Based Graphical Models
We employ model assisted clustering, in which the clusters contain features that are similar to the same unobserved latent variable.
A fast algorithm with minimax optimal guarantees for topic models with an unknown number of topics
We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data.
Adaptive Estimation in Structured Factor Models with Applications to Overlapping Clustering
This work introduces a novel estimation method, called LOVE, of the entries and structure of a loading matrix A in a sparse latent factor model X = AZ + E, for an observable random vector X in Rp, with correlated unobservable factors Z \in RK, with K unknown, and independent noise E. Each row of A is scaled and sparse.
PECOK: a convex optimization approach to variable clustering
The problem of variable clustering is that of grouping similar components of a $p$-dimensional vector $X=(X_{1},\ldots, X_{p})$, and estimating these groups from $n$ independent copies of $X$.
Statistics Theory Statistics Theory
Model Assisted Variable Clustering: Minimax-optimal Recovery and Algorithms
We quantify the difficulty of clustering data generated from a G-block covariance model in terms of cluster proximity, measured with respect to two related, but different, cluster separation metrics.
Convex Banding of the Covariance Matrix
Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results.
