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Found 28 papers, 5 papers with code
Adaptive Split Balancing for Optimal Random Forest
While random forests are commonly used for regression problems, existing methods often lack adaptability in complex situations or lose optimality under simple, smooth scenarios.
Optimal vintage factor analysis with deflation varimax
Vintage factor analysis is one important type of factor analysis that aims to first find a low-dimensional representation of the original data, and then to seek a rotation such that the rotated low-dimensional representation is scientifically meaningful.
The Decaying Missing-at-Random Framework: Doubly Robust Causal Inference with Partially Labeled Data
Notably, we relax the need for a positivity condition, commonly required in the missing data literature, and allow uniform decay of labeling propensity scores with sample size, accommodating faster growth of unlabeled data.
A Geometric Approach to $k$-means
This framework consists of alternating between the following two steps iteratively: (i) detect mis-specified clusters in a local solution and (ii) improve the current local solution by non-local operations.
Dynamic treatment effects: high-dimensional inference under model misspecification
This paper introduces a new approach by proposing novel, robust estimators for both treatment assignments and outcome models.
High-dimensional Inference for Dynamic Treatment Effects
Estimating dynamic treatment effects is a crucial endeavor in causal inference, particularly when confronted with high-dimensional confounders.
Unique sparse decomposition of low rank matrices
In this paper, we study the problem of seeking a unique decomposition of a low rank matrix $Y\in \mathbb{R}^{p\times n}$ that admits a sparse representation.
Double Robust Semi-Supervised Inference for the Mean: Selection Bias under MAR Labeling with Decaying Overlap
Apart from a moderate-sized labeled data, L, the SS setting is characterized by an additional, much larger sized, unlabeled data, U.
Local Minima Structures in Gaussian Mixture Models
As the objective function is non-convex, there can be multiple local minima that are not globally optimal, even for well-separated mixture models.
Low-rank matrix recovery with non-quadratic loss: projected gradient method and regularity projection oracle
Existing results for low-rank matrix recovery largely focus on quadratic loss, which enjoys favorable properties such as restricted strong convexity/smoothness (RSC/RSM) and well conditioning over all low rank matrices.
From Symmetry to Geometry: Tractable Nonconvex Problems
We highlight the key role of symmetry in shaping the objective landscape and discuss the different roles of rotational and discrete symmetries.
Geometric Analysis of Nonconvex Optimization Landscapes for Overcomplete Learning
Learning overcomplete representations finds many applications in machine learning and data analytics.
Short and Sparse Deconvolution --- A Geometric Approach
Short-and-sparse deconvolution (SaSD) is the problem of extracting localized, recurring motifs in signals with spatial or temporal structure.
Structures of Spurious Local Minima in $k$-means
Our theoretical results corroborate existing empirical observations and provide justification for several improved algorithms for $k$-means clustering.
Polynomial Matrix Completion for Missing Data Imputation and Transductive Learning
This paper develops new methods to recover the missing entries of a high-rank or even full-rank matrix when the intrinsic dimension of the data is low compared to the ambient dimension.
Analysis of the Optimization Landscapes for Overcomplete Representation Learning
In this work, we show these problems can be formulated as $\ell^4$-norm optimization problems with spherical constraint, and study the geometric properties of their nonconvex optimization landscapes.
Short-and-Sparse Deconvolution -- A Geometric Approach
This paper is motivated by recent theoretical advances, which characterize the optimization landscape of a particular nonconvex formulation of SaSD.
Global Convergence of Least Squares EM for Demixing Two Log-Concave Densities
This work studies the location estimation problem for a mixture of two rotation invariant log-concave densities.
High-dimensional semi-supervised learning: in search for optimal inference of the mean
We provide a high-dimensional semi-supervised inference framework focused on the mean and variance of the response.
On the Global Geometry of Sphere-Constrained Sparse Blind Deconvolution
Blind deconvolution is the problem of recovering a convolutional kernel $\boldsymbol a_0$ and an activation signal $\boldsymbol x_0$ from their convolution $\boldsymbol y = \boldsymbol a_0 \circledast \boldsymbol x_0$.
Geometry and Symmetry in Short-and-Sparse Deconvolution
We study the $\textit{Short-and-Sparse (SaS) deconvolution}$ problem of recovering a short signal $\mathbf a_0$ and a sparse signal $\mathbf x_0$ from their convolution.
Structured Local Minima in Sparse Blind Deconvolution
We assume the short signal to have unit $\ell^2$ norm and cast the blind deconvolution problem as a nonconvex optimization problem over the sphere.
Structured Local Optima in Sparse Blind Deconvolution
We assume the short signal to have unit $\ell^2$ norm and cast the blind deconvolution problem as a nonconvex optimization problem over the sphere.
Convolutional Phase Retrieval via Gradient Descent
We study the convolutional phase retrieval problem, of recovering an unknown signal $\mathbf x \in \mathbb C^n $ from $m$ measurements consisting of the magnitude of its cyclic convolution with a given kernel $\mathbf a \in \mathbb C^m $.
Convolutional Phase Retrieval
We study the convolutional phase retrieval problem, which asks us to recover an unknown signal ${\mathbf x} $ of length $n$ from $m$ measurements consisting of the magnitude of its cyclic convolution with a known kernel $\mathbf a$ of length $m$.
Scalable Robust Matrix Recovery: Frank-Wolfe Meets Proximal Methods
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning.
Toward Guaranteed Illumination Models for Non-Convex Objects
Illumination variation remains a central challenge in object detection and recognition.
Efficient Point-to-Subspace Query in $\ell^1$ with Application to Robust Object Instance Recognition
Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image), efficiently determine the nearest subspace to the query in $\ell^1$ distance.
