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Nested dropout is a variant of dropout operation that is able to order network parameters or features based on the pre-defined importance during training. It has been explored for: I. Constructing nested nets: the nested nets are neural…
This paper addresses the problem of nearly optimal Vapnik--Chervonenkis dimension (VC-dimension) and pseudo-dimension estimations of the derivative functions of deep neural networks (DNNs). Two important applications of these estimations…
We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications,…
Laws of large numbers guarantee that given a large enough sample from some population, the measure of any fixed sub-population is well-estimated by its frequency in the sample. We study laws of large numbers in sampling processes that can…
Originally designed for applications in computer graphics, visual computing (VC) methods synthesize information about physical and virtual worlds, using prescribed algorithms optimized for spatial computing. VC is used to analyze geometry,…
Visual Transformers (VTs) are emerging as an architectural paradigm alternative to Convolutional networks (CNNs). Differently from CNNs, VTs can capture global relations between image elements and they potentially have a larger…
We introduce a new method for high-dimensional, online changepoint detection in settings where a $p$-variate Gaussian data stream may undergo a change in mean. The procedure works by performing likelihood ratio tests against simple…
Visual patterns represent the discernible regularity in the visual world. They capture the essential nature of visual objects or scenes. Understanding and modeling visual patterns is a fundamental problem in visual recognition that has wide…
We propose an online learning algorithm for a class of machine learning models under a separable stochastic approximation framework. The essence of our idea lies in the observation that certain parameters in the models are easier to…
The consensus problem -- achieving agreement among a network of agents -- is a central theme in both theory and applications. Recently, this problem has been extended from Euclidean spaces to the space of probability measures, where the…
Metric-based meta-learning has attracted a lot of attention due to its effectiveness and efficiency in few-shot learning. Recent studies show that metric scaling plays a crucial role in the performance of metric-based meta-learning…
We present the principle and the main steps of a new method for the visuo-spatial analysis of geometrical sketches recorded online. Visuo-spatial analysis is a necessary step for multi-level analysis. Multi-level analysis simultaneously…
The disjointness problem - where Alice and Bob are given two subsets of $\{1, \dots, n\}$ and they have to check if their sets intersect - is a central problem in the world of communication complexity. While both deterministic and…
Many machine learning applications deal with high dimensional data. To make computations feasible and learning more efficient, it is often desirable to reduce the dimensionality of the input variables by finding linear combinations of the…
Many existing algorithms for streaming geometric data analysis have been plagued by exponential dependencies in the space complexity, which are undesirable for processing high-dimensional data sets. In particular, once $d\geq\log n$, there…
For many important network types (e.g., sensor networks in complex harsh environments and social networks) physical coordinate systems (e.g., Cartesian), and physical distances (e.g., Euclidean), are either difficult to discern or…
In the classical online model, the maximum independent set problem admits an $\Omega(n)$ lower bound on the competitive ratio even for interval graphs, motivating the study of the problem under additional assumptions. We first study the…
This paper addresses the problem of online learning in a dynamic setting. We consider a social network in which each individual observes a private signal about the underlying state of the world and communicates with her neighbors at each…
As the network slicing is one of the critical enablers in communication networks, one anomalous physical node (PN) or physical link (PL) in substrate networks that carries multiple virtual network elements can cause significant performance…
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques,…