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The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an…
There are several ways to measure the compressibility of a random measure; they include general approaches such as using the rate-distortion curve, as well as more specific notions, such as the Renyi information dimension (RID). The RID…
When auditing a redistricting plan, a persuasive method is to compare the plan with an ensemble of neutrally drawn redistricting plans. Ensembles are generated via algorithms that sample distributions on balanced graph partitions. To audit…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
In Robotics, especially in this era of autonomous driving, mapping is one key ability of a robot to be able to navigate through an environment, localize on it and analyze its traversability. To allow for real-time execution on constrained…
Embedding representations power machine intelligence in many applications, including recommendation systems, but they are space intensive -- potentially occupying hundreds of gigabytes in large-scale settings. To help manage this outsized…
The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…
Data quantization learns encoding results of data with certain requirements, and provides a broad perspective of many real-world applications to data handling. Nevertheless, the results of encoder is usually limited to multivariate inputs…
Deep networks are successfully used as classification models yielding state-of-the-art results when trained on a large number of labeled samples. These models, however, are usually much less suited for semi-supervised problems because of…
The expicit restricted isometry property (RIP) measurement matrices are needed in practical application of compressed sensing in signal processing. RIP matrices from Reed-Solomon codes, BCH codes, orthogonal codes, expander graphs have been…
The Johnson-Lindenstrauss transform allows one to embed a dataset of $n$ points in $\mathbb{R}^d$ into $\mathbb{R}^m,$ while preserving the pairwise distance between any pair of points up to a factor $(1 \pm \varepsilon)$, provided that $m…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
It is demonstrated how linear computational time and storage efficient approaches can be adopted when analyzing very large data sets. More importantly, interpretation is aided and furthermore, basic processing is easily supported. Such…
Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…
Deep neural networks (DNNs) are ubiquitous in computer vision and natural language processing, but suffer from high inference cost. This problem can be addressed by quantization, which consists in converting floating point perations into a…
We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a…
Deep metrics have been shown effective as similarity measures in multi-modal image registration; however, the metrics are currently constructed from aligned image pairs in the training data. In this paper, we propose a strategy for learning…
A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many…
Information theoretical measures, such as entropy, mutual information, and various divergences, exhibit robust characteristics in image registration applications. However, the estimation of these quantities is computationally intensive in…
Time-varying mixture densities occur in many scenarios, for example, the distributions of keywords that appear in publications may evolve from year to year, video frame features associated with multiple targets may evolve in a sequence. Any…