相关论文: Optimally compressing VC classes
Suppose there is a large file which should be transmitted (or stored) and there are several (say, m) admissible data-compressors. It seems natural to try all the compressors and then choose the best, i.e. the one that gives the shortest…
We propose a method for estimating a covariance matrix that can be represented as a sum of a low-rank matrix and a diagonal matrix. The proposed method compresses high-dimensional data, computes the sample covariance in the compressed…
We extend our work for compression of currents and varifolds to a compression algorithm for the embedded normal cycles representation of shape, restricted to the constant normal kernel case, using the Nystrom approximation in Reproducing…
Video Coding for Machines (VCM) is committed to bridging to an extent separate research tracks of video/image compression and feature compression, and attempts to optimize compactness and efficiency jointly from a unified perspective of…
We propose a data reduction technique for scattered data based on statistical sampling. Our void-and-cluster sampling technique finds a representative subset that is optimally distributed in the spatial domain with respect to the blue noise…
We formulate the problem of performing optimal data compression under the constraints that compressed data can be used for accurate classification in machine learning. We show that this translates to a problem of minimizing the mutual…
Reducing acquisition time is a crucial challenge for many imaging techniques. Compressed Sensing (CS) theory offers an appealing framework to address this issue since it provides theoretical guarantees on the reconstruction of sparse…
We provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper.The…
In this paper we construct a model for the classifying space, BVCG, of a crystallographic group G of rank n relative to the family VC of virtually-cyclic subgroups of G. The model is used to show that there exists no other model for the…
This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…
VC-dimension and $\varepsilon$-nets are key concepts in Statistical Learning Theory. Intuitively, VC-dimension is a measure of the size of a class of sets. The famous $\varepsilon$-net theorem, a fundamental result in Discrete Geometry,…
This paper discusses the topic of dimensionality reduction for $k$-means clustering. We prove that any set of $n$ points in $d$ dimensions (rows in a matrix $A \in \RR^{n \times d}$) can be projected into $t = \Omega(k / \eps^2)$…
Consider the problem of reconstructing a multidimensional signal from an underdetermined set of measurements, as in the setting of compressed sensing. Without any additional assumptions, this problem is ill-posed. However, for signals such…
The problem of compressing a real-valued sparse source using compressive sensing techniques is studied. The rate distortion optimality of a coding scheme in which compressively sensed signals are quantized and then reconstructed is…
Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…
For high volume data streams and large data warehouses, sampling is used for efficient approximate answers to aggregate queries over selected subsets. Mathematically, we are dealing with a set of weighted items and want to support queries…
We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…
The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…
A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change…
In this paper we investigate a class of (d+1) dimensional cosmological models with a cosmological constant possessing an R^d simply transitive symmetry group and show that it can be written in a form that manifests the effect of a…