arXiv research

New findings on robust learning with well-separated data.

The moduli space metric and its Kahler potential for well-separated non-Abelian vortices are obtained in U(N) gauge theories with N Higgs fields in the fundamental representation.

We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point. These estimates can then be clustered using, for example, $k$-means. For problem…

Stochastic Neighbor Embedding and its variants are widely used dimensionality reduction techniques -- despite their popularity, no theoretical results are known. We prove that the optimal SNE embedding of well-separated clusters from high dimensions to any Euclidean space R^d manages to successfully separate the cluste…

We analyze the spectral clustering procedure for identifying coarse structure in a data set $x_1, \dots, x_n$, and in particular study the geometry of graph Laplacian embeddings which form the basis for spectral clustering algorithms. More precisely, we assume that the data is sampled from a mixture model supported on …

This study examines when non-parametric methods are robust to adversarial examples.

Improved sample efficiency with normalized RBF kernels in neural networks.

Consistent estimator for mixtures of nonparametric elliptical distributions helps cluster analysis.

We consider the problem of spherical Gaussian Mixture models with $k \geq 3$ components when the components are well separated. A fundamental previous result established that separation of $Ω(\sqrt{\log k})$ is necessary and sufficient for identifiability of the parameters with polynomial sample complexity (Regev and V…

New method estimates density ratio for well-separated distributions using multi-class logistic regression.

Algorithm distinguishes Gaussian mixtures from pure Gaussians in quasi-polynomial time.

At critical coupling, the interactions of Ginzburg-Landau vortices are determined by the metric on the moduli space of static solutions. The asymptotic form of the metric for two well separated vortices is shown here to be expressible in terms of a Bessel function. A straightforward extension gives the metric for N vor…

Recent progress has shown that few-shot learning can be improved with access to unlabelled data, known as semi-supervised few-shot learning(SS-FSL). We introduce an SS-FSL approach, dubbed as Prototypical Random Walk Networks(PRWN), built on top of Prototypical Networks (PN). We develop a random walk semi-supervised lo…

Researchers create initial data for multiple collapsing boson stars.

Constructs classifiers for neural networks with specific data configurations.

Constructs initial data for multiple black holes with specified ADM parameters.

New algorithm learns POMDPs without computational oracles.

Neural networks have many successful applications, while much less theoretical understanding has been gained. Towards bridging this gap, we study the problem of learning a two-layer overparameterized ReLU neural network for multi-class classification via stochastic gradient descent (SGD) from random initialization. In …

The paper analyzes the risk of CV-tuned regularized estimators and connects it to SURE.

The main contribution of the paper is to show that Gaussian sketching of a kernel-Gram matrix $\boldsymbol K$ yields an operator whose counterpart in an RKHS $\mathcal H$, is a \emph{random projection} operator---in the spirit of Johnson-Lindenstrauss (J-L) lemma. To be precise, given a random matrix $Z$ with i.i.d. Ga…

A new approach clusters data first, then embeds each cluster, improving transparency.

We investigate the problem of nodes clustering under privacy constraints when representing a dataset as a graph. Our contribution is threefold. First we formally define the concept of differential privacy for structured databases such as graphs, and give an alternative definition based on a new neighborhood notion betw…

Relative moduli spaces of periodic monopoles provide novel examples of Asymptotically Locally Flat hyperkahler manifolds. By considering the interactions between well-separated periodic monopoles, we infer the asymptotic behavior of their metrics. When the monopole moduli space is four-dimensional, this construction yi…

Paper proposes a novel unsupervised feature selection method using K-means and ADMM.

Suppose M is a compact orientable irreducible 3-manifold with Heegaard splitting surfaces P and Q. Then either Q is isotopic to a possibly stabilized copy of P or the Hempel distance of the splitting P is no greater than twice the genus of Q. More generally, if P and Q are bicompressible but weakly incompressible conne…

Improved sample complexity for Gaussian process approximations.

New algorithm for planning in observable POMDPs in quasi-polynomial time.

Sparse subspace clustering (SSC) is an elegant approach for unsupervised segmentation if the data points of each cluster are located in linear subspaces. This model applies, for instance, in motion segmentation if some restrictions on the camera model hold. SSC requires that problems based on the $l_1$-norm are solved …

Neural networks can interpolate noisy data and still generalize well.

Density-based clustering is the task of discovering high-density regions of entities (clusters) that are separated from each other by contiguous regions of low-density. DBSCAN is, arguably, the most popular density-based clustering algorithm. However, its cluster recovery capabilities depend on the combination of the t…

Irregular features disrupt the desired classification. In this paper, we consider aggressively modifying scales of features in the original space according to the label information to form well-separated clusters in low-dimensional space. The proposed method exploits spectral clustering to derive scaling factors that a…

On a complete manifold, such as Euclidean 3-space or hyperbolic 3-space, the limit at infinity of the norm of the Higgs field is called the mass of the monopole. We show the existence, on hypebolic 3-space, of monopoles with given magnetic charge and arbitrary mass. Previously, aside from charge one monopoles, existenc…

Develops method to train classifiers on incomplete feature datasets.

KPCA improves OoD detection by separating InD and OoD data.

Learning the parameters of Gaussian mixture models is a fundamental and widely studied problem with numerous applications. In this work, we give new algorithms for learning the parameters of a high-dimensional, well separated, Gaussian mixture model subject to the strong constraint of differential privacy. In particula…

Deep neural networks (DNNs) have achieved exceptional performances in many tasks, particularly, in supervised classification tasks. However, achievements with supervised classification tasks are based on large datasets with well-separated classes. Typically, real-world applications involve wild datasets that include si…

DNLL loss improves deep LDA accuracy and consistency.

In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them, it's important to know if they are connected or well separated from each other. The main focus of this paper is discovering the relations between the resulting clusters. We propose a new method which is based …

Adv-SSL learns unbiased representations from unlabeled data with theoretical guarantees.

We inspect a possible clustering structure of the corruption perception among 134 countries. Using the average linkage clustering, we uncover a well-defined hierarchy in the relationships among countries. Four main clusters are identified and they suggest that countries worldwide can be quite well separated according t…

New indices for determining cluster compactness and separability.

We present a simple noise-robust margin-based active learning algorithm to find homogeneous (passing the origin) linear separators and analyze its error convergence when labels are corrupted by noise. We show that when the imposed noise satisfies the Tsybakov low noise condition (Mammen, Tsybakov, and others 1999; Tsyb…

GC-Flow uses graph flows for better clustering than traditional GCNs.

Adaptive clustering and personalization algorithms minimize regret in multi-agent stochastic linear bandits.

A new Wasserstein $K$-means method for clustering probability distributions.

Random feature matrices' singular values concentrate near their full expectation in high dimensions.

Sparse subspace clustering (SSC) using greedy-based neighbor selection, such as matching pursuit (MP) and orthogonal matching pursuit (OMP), has been known as a popular computationally-efficient alternative to the conventional L1-minimization based methods. Under deterministic bounded noise corruption, in this paper we…

Single neural network learns multiple tasks from combined data.