The fashion industry has been identified as a major contributor to waste and emissions, leading to an increased interest in promoting the second-hand market. Machine learning methods play an important role in facilitating the creation and expansion of second-hand marketplaces by enabling the large-scale valuation of used garments. We contribute to this line of work by addressing the scalability of second-hand image retrieval from databases. By introducing a selective representation framework, we can shrink databases to 10% of their original size without sacrificing retrieval accuracy. We first explore clustering and coreset selection methods to identify representative samples that capture the key features of each garment and its internal variability. Then, we introduce an efficient outlier removal method, based on a neighbour-homogeneity consistency score measure, that filters out uncharacteristic samples prior to selection. We evaluate our approach on three public datasets: DeepFashion Attribute, DeepFashion Con2Shop, and DeepFashion2. The results demonstrate a clear performance-efficiency trade-off by strategically pruning and selecting representative vectors of images. The retrieval system maintains near-optimal accuracy, while greatly reducing computational costs by reducing the images added to the vector database. Furthermore, applying our outlier removal method to clustering techniques yields even higher retrieval performance by removing non-discriminative samples before the selection.

Estimating Mutual Information (MI), a key measure of dependence of random quantities without specific modeling assumptions, is a challenging problem in high dimensions. We propose a novel mutual information estimator based on parametrizing conditional densities using normalizing flows, a deep generative model that has gained popularity in recent years. This estimator leverages a block autoregressive structure to achieve improved bias-variance trade-offs on standard benchmark tasks.

SUMMARY: vSPACE is a web-based application presenting a spatial representation of scRNAseq data obtained from human articular cartilage by emulating the concept of spatial transcriptomics technology, but virtually. This virtual 2D plot presentation of human articular cartage cells generates several zonal distribution patterns, for one or multiple genes at a time, revealing patterns that scientists can appreciate as imputed spatial distribution patterns along the zonal axis. AVAILABILITY AND IMPLEMENTATION: vSPACE is implemented in Python Dash as a web-based toolbox designed for data visualization of zonal gene expression patterns in articular cartilage chondrocytes. This tool is freely accessible at: https://vspace.cse.uconn.edu/The source code and extra materials for this service can be downloaded from: https://github.com/zhacheny/vSPACE.

Given a set P of n points and a constant k, we are interested in computing the persistent homology of the Čech filtration of P for the k-distance, and investigate the effectiveness of dimensionality reduction for this problem, answering an open question of Sheehy [Proc. SoCG, 2014]. We show that any linear transformation that preserves pairwise distances up to a (1±ε) multiplicative factor, must preserve the persistent homology of the Čech filtration up to a factor of (1-ε)^{-1}. Our results also show that the Vietoris-Rips and Delaunay filtrations for the k-distance, as well as the Čech filtration for the approximate k-distance of Buchet et al. are preserved up to a (1±ε) factor. We also prove extensions of our main theorem, for point sets (i) lying in a region of bounded Gaussian width or (ii) on a low-dimensional manifold, obtaining the target dimension bounds of Lotz [Proc. Roy. Soc. , 2019] and Clarkson [Proc. SoCG, 2008 ] respectively.

We derive bounds relating the statistical dimension of linear images of convex cones to Renegar's condition number. Using results from conic integral geometry, we show that the bounds can be made to depend only on a random projection to a lower dimensional space, and can still be effective if the linear maps are ill-conditioned. As an application, we get new bounds for the undersampling phase transition of composite convex regularizers. Key tools in the analysis are Slepian's inequality, interpreted as monotonicity property of moment functionals, and the kinematic formula from integral geometry. The main results are derived in the generalized setting of the biconic homogeneous feasibility problem.

Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and it has become standard to replace it with an upper-bound. To ensure that this technique is suitable, [1] has introduced an upper-bound on the gap between the statistical dimension and its approximation. In this work, we first show that the error bound in [1] in some low-dimensional models such as total variation and ℓ1analysis minimization becomes poorly large. Next, we develop a new error bound which significantly improves the estimation gap compared to [1]. In particular, unlike the bound in [1] that fails in some settings with overcomplete dictionaries, our bound exhibits a decaying behavior in such cases.

The theory of intrinsic volumes of convex cones has recently found striking applications in areas such as convex optimization and compressive sensing. This article provides a self-contained account of the combinatorial theory of intrinsic volumes for polyhedral cones. Direct derivations of the general Steiner formula, the conic analogues of the Brianchon–Gram–Euler and the Gauss–Bonnet relations, and the principal kinematic formula are given. In addition, a connection between the characteristic polynomial of a hyperplane arrangement and the intrinsic volumes of the regions of the arrangement, due to Klivans and Swartz, is generalized and some applications are presented.

We prove lower bounds of order n log n for both the problem of multiplying polynomials of degree n , and of dividing polynomials with remainder, in the model of bounded coefficient arithmetic circuits over the complex numbers. These lower bounds are optimal up to order of magnitude. The proof uses a recent idea of R. Raz [ Proc. 34th STOC 2002 ] proposed for matrix multiplication. It reduces the linear problem of multiplying a random circulant matrix with a vector to the bilinear problem of cyclic convolution. We treat the arising linear problem by extending J. Morgenstern's bound [ J. ACM 20, pp. 305--306, 1973 ] in a unitarily invariant way. This establishes a new lower bound on the bounded coefficient complexity of linear forms in terms of the singular values of the corresponding matrix. In addition, we extend these lower bounds for linear and bilinear maps to a model of circuits that allows a restricted number of unbounded scalar multiplications.

We prove lower bounds of order n log n for both the problem to multiply polynomials of degree n, and to divide polynomials with remainder, in the model of bounded coefficient arithmetic circuits over the complex numbers. These lower bounds are optimal up to order of magnitude. The proof uses a recent idea of R. Raz [Proc. 34th STOC 2002] proposed for matrix multiplication. It reduces the linear problem to multiply a random circulant matrix with a vector to the bilinear problem of cyclic convolution. We treat the arising linear problem by extending J. Morgenstern's bound [J. ACM 20, pp. 305-306, 1973] in a unitarily invariant way. This establishes a new lower bound on the bounded coefficient complexity of linear forms in terms of the singular values of the corresponding matrix.