arXiv research

The paper extends risk measures to two-step approximations and studies log-concave distributions.

Study extends learnability equivalence to multi-class and regression, overcoming binary classification limits.

Improved bounds on combining hypothesis classes for binary functions.

Let $M$ be a compact, unit volume, Riemannian manifold with boundary. In this paper we study the homology of a random Čech-complex generated by a homogeneous Poisson process in $M$. Our main results are two asymptotic threshold formulas, an upper threshold above which the Čech complex recovers the $k$-th homology of $M…

Random projections improve classifier generalization without needing to choose the best threshold.

Contradiction graphs reveal VC dimension threshold.

Polynomial neural networks explore thresholds for maximum expressiveness.

Study on discrete Okounkov bodies and their applications.

The Gaussian process latent variable model (GP-LVM) is a popular approach to non-linear probabilistic dimensionality reduction. One design choice for the model is the number of latent variables. We present a spike and slab prior for the GP-LVM and propose an efficient variational inference procedure that gives a lower …

This study optimizes multi-modal learning thresholds and algorithms in high dimensions.

In this paper, we study the problem of estimating the covariance matrix under differential privacy, where the underlying covariance matrix is assumed to be sparse and of high dimensions. We propose a new method, called DP-Thresholding, to achieve a non-trivial $\ell_2$-norm based error bound, which is significantly bet…

Optimal algorithm for identifying best arm in stochastic linear bandits with fixed confidence.

New framework models echo chamber learning, proving tight bounds on algorithm performance.

Extends wealth tax neutrality framework to stochastic volatility and non-homothetic preferences.

Paper discusses new stochastic algorithms for sparse signal recovery.

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity clustering algorithm based on thresholding the correlations between the data po…

Quadratic regression involves modeling the response as a (generalized) linear function of not only the features $x^{j_1}$ but also of quadratic terms $x^{j_1}x^{j_2}$. The inclusion of such higher-order "interaction terms" in regression often provides an easy way to increase accuracy in already-high-dimensional problem…

The article examines different thresholding methods for improving PAM algorithm in cancer classification.

In this paper, we consider the problem of compressed sensing where the goal is to recover almost all the sparse vectors using a small number of fixed linear measurements. For this problem, we propose a novel partial hard-thresholding operator that leads to a general family of iterative algorithms. While one extreme of …

Sparse reconstruction approaches using the re-weighted l1-penalty have been shown, both empirically and theoretically, to provide a significant improvement in recovering sparse signals in comparison to the l1-relaxation. However, numerical optimization of such penalties involves solving problems with l1-norms in the ob…

Improved Sparse Polyak for high-dimensional M-estimation with sparser solutions.

The study explores the compressive power of Boolean threshold autoencoders, finding that seven layers are necessary but three are not.

Training neural networks is hard in fixed dimensions.

The paper characterizes spin initial data sets saturating the BPS bound in asymptotically AdS spacetimes.

Metalearning optimizes autoencoder dimensions for efficient data representation.

New algorithm detects communities even with corrupted data, reaching Kesten-Stigum threshold.

Fewer degrees of freedom can train deep networks, showing a sharp phase transition.

We investigate the impact of available information on the estimation of the default probability within a generalized structural model for credit risk. The traditional structural model where default is triggered when the value of the firm's asset falls below a constant threshold is extended by relaxing the assumption of…

We show that for a K-unstable Fano variety, any divisorial valuation computing its stability threshold induces a non-trivial special test configuration preserving the stability threshold. When such a divisorial valuation exists, we show that the Fano variety degenerates to a uniquely determined twisted K-polystable Fan…

Study shows large extra dimensions are hidden from view by black holes.

Proves finitely generated associated graded rings for valuations on log Fano pairs.

New method corrects Laplace/BIC errors in singular models, revealing effective dimension.

A fast method estimates Gaussian mixture components without iterative fitting.

This work proves DP learnability implies online learnability for general classification tasks.

Reverse Hölder inequalities on Fano metrics with applications to geodesics and singularities.

Paper develops algorithms to maximize AUC in imbalanced classification.

Study shows boundedness of klt singularities in 3D or with bounded Kollár components.

This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into account their sparse nature. Assuming that the system is stable, or that it is eq…

Characterizes optimal reconstruction error in high-dimensional Gaussian mixtures.

Monotone neural networks can approximate and interpolate functions efficiently.

Unified framework for shrinkage, thresholding, and regularization in normal mean estimation and linear regression.

Recently, a novel family of biologically plausible online algorithms for reducing the dimensionality of streaming data has been derived from the similarity matching principle. In these algorithms, the number of output dimensions can be determined adaptively by thresholding the singular values of the input data matrix. …

We show that every approximately differentially private learning algorithm (possibly improper) for a class $H$ with Littlestone dimension~$d$ requires $Ω\bigl(\log^*(d)\bigr)$ examples. As a corollary it follows that the class of thresholds over $\mathbb{N}$ can not be learned in a private manner; this resolves open qu…

We consider the problem of clustering noisy high-dimensional data points into a union of low-dimensional subspaces and a set of outliers. The number of subspaces, their dimensions, and their orientations are unknown. A probabilistic performance analysis of the thresholding-based subspace clustering (TSC) algorithm intr…

We study graph matching with correlated Gaussian features and find thresholds for exact recovery.

In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for Singular Value Decomposition (STAT-SVD) is proposed. The proposed procedure featu…

Optimal classifiers derived from GMMs are approximated by deep neural networks.

Thresholded Lasso bandit minimizes regret in sparse linear bandits.