A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A faster Wasserstein k-means algorithm for histogram data reduces computation and maintains clustering quality.
Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the -norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank a…
Iterative hard thresholding (IHT) is a projected gradient descent algorithm, known to achieve state of the art performance for a wide range of structured estimation problems, such as sparse inference. In this work, we consider IHT as a solution to the problem of learning sparse discrete distributions. We study the hard…
High dimensional sparse learning has imposed a great computational challenge to large scale data analysis. In this paper, we are interested in a broad class of sparse learning approaches formulated as linear programs parametrized by a {\em regularization factor}, and solve them by the parametric simplex method (PSM). O…
We provide an elementary proof of a simple, efficient algorithm for computing the Euclidean projection of a point onto the probability simplex. We also show an application in Laplacian K-modes clustering.
Estimates dimensions of maximal simplices for rational and irrational trees in Outer space.
Moment polytope of toric exponential families is a projection of a simplex.
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the positive orthant of the unit sphere. This measure gathers information on the localizat…
Unfolding paths in Outer space accumulate on a simplex, not converge.
Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space the time-discret…
A new optimization method for probability simplex problems.
A new GP inference method using simplices for high-dimensional data.
CASP improves portfolio optimization by considering asset covariance.
A new geometry-preserving method for interpreting compositional data.
This article presents an improvement and extension of the heuristic first presented by Hougardy, Lutz, and Zelke in 2010 for realizing triangulated orientable surfaces with few vertices by a simplex-wise linear embedding. The improvement consists in the applicability to non-orientable surfaces (simplex-wise linear imme…
In this paper we present two new approaches to efficiently solve large-scale compressed sensing problems. These two ideas are independent of each other and can therefore be used either separately or together. We consider all possibilities. For the first approach, we note that the zero vector can be taken as the initial…
Introduces a new geometric framework for probability distributions.
This paper introduces Laplace techniques for designing a neural network, with the goal of estimating simplex-constraint sparse vectors from compressed measurements. To this end, we recast the problem of MMSE estimation (w.r.t. a pre-defined uniform input distribution) as the problem of computing the centroid of some po…
GOPO optimizes large models in Hilbert space, avoiding Kullback-Leibler's curvature.
The paper triangulates Heisenberg groups with horizontal and straight simplexes.
The paper develops formulas for hyperbolic simplices based on edge lengths.
Study classifies submanifolds in probability simplex.
Locality regularized reconstruction finds sparse coefficients for sparse and structured data.
Study optimal transport on simplex boundary, proving transport map and potential regularity.
Random projections help in representing sparse graphs efficiently.
Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS theory is based on random Gaussian projection matrices, which satisfy recovery guara…
A new method for approximating softmax and Gaussian kernels with reduced error.
Efficiently projects points onto polytopes, especially useful in web-scale applications.
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 algorithms for approximate inference via information projection that are applica…
The Bezier simplex fitting is a novel data modeling technique which exploits geometric structures of data to approximate the Pareto front of multi-objective optimization problems. There are two fitting methods based on different sampling strategies. The inductive skeleton fitting employs a stratified subsampling from e…
PRISM identifies simplex vertices from noisy data.
We establish the second part of Milnor's conjecture on the volume of simplexes in hyperbolic and spherical spaces. A characterization of the closure of the space of the angle Gram matrices of simplexes is also obtained.
New algorithm uses random projections for robust, sparse data classification.
A hyperbolic 3-simplex reflection group is a Coxeter group arising as a lattice in the isometry group of hyperbolic 3-space, with fundamental domain a geodesic simplex (possibly with some ideal vertices). The classification of these groups is known, and there are exactly 9 cocompact examples, and 23 non-cocompact examp…
We introduce the non-pure versions of simplicial balls and spheres with minimum number of vertices. These are a special type of non-homogeneous balls and spheres (NH-balls and NH-spheres) satisfying a minimality condition on the number of maximal simplices. The main result is that minimal NH-balls and NH-spheres are pr…
In 1973, J. Cheeger and J. Simons raised the following question that still remains open and is known as the Rational Simplex Problem: Given a geodesic simplex in the spherical 3-space so that all of its interior dihedral angles are rational multiples of , is it true that its volume is a rational multiple of the volu…
New algorithm improves sparse-view tomography without needing ground-truth data.
We consider a class of linear-programming based estimators in reconstructing a sparse signal from linear measurements. Specific formulations of the reconstruction problem considered here include Dantzig selector, basis pursuit (for the case in which the measurements contain no errors), and the fused Dantzig selector (f…
Simple Deep LDA models achieve accuracy competitive with softmax baselines.
We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's function may be recovered from seismic experimental data using sparsity optimization…
Inspired by the advances in biological science, the study of sparse binary projection models has attracted considerable recent research attention. The models project dense input samples into a higher-dimensional space and output sparse binary data representations after the Winner-Take-All competition, subject to the co…
A method for diffusion on probability simplex for generative models.
The big data trend has inspired feature-driven learning tasks, which cannot be handled by conventional machine learning models. Unstructured data produces very large binary matrices with millions of columns when converted to vector form. However, such data is often sparse, and hence can be manageable through the use of…
New method selects variables for GP regression using sparse projection.
Performing signal processing tasks on compressive measurements of data has received great attention in recent years. In this paper, we extend previous work on compressive dictionary learning by showing that more general random projections may be used, including sparse ones. More precisely, we examine compressive K-mean…
When applying principal component analysis (PCA) for dimension reduction, the most varying projections are usually used in order to retain most of the information. For the purpose of anomaly and change detection, however, the least varying projections are often the most important ones. In this article, we present a nov…
Concrete distribution properties examined on simplex.
This paper deals with unsupervised clustering with feature selection. The problem is to estimate both labels and a sparse projection matrix of weights. To address this combinatorial non-convex problem maintaining a strict control on the sparsity of the matrix of weights, we propose an alternating minimization of the Fr…