Related papers: Computationally Efficient Learning of Statistical …
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
We address distributed learning problems, both nonconvex and convex, over undirected networks. In particular, we design a novel algorithm based on the distributed Alternating Direction Method of Multipliers (ADMM) to address the challenges…
Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…
Fusion and inference from multiple and massive disparate data sources - the requirement for our most challenging data analysis problems and the goal of our most ambitious statistical pattern recognition methodologies - -has many and varied…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…
We consider the problem of finding high dimensional approximate nearest neighbors. Suppose there are d independent rare features, each having its own independent statistics. A point x will have x_{i}=0 denote the absence of feature i, and…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known…
This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…
The manifold hypothesis suggests that high-dimensional data often lie on or near a low-dimensional manifold. Estimating the dimension of this manifold is essential for leveraging its structure, yet existing work on dimension estimation is…
Learning the embedding space, where semantically similar objects are located close together and dissimilar objects far apart, is a cornerstone of many computer vision applications. Existing approaches usually learn a single metric in the…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
In this research, we introduce the concept of "computational entanglement," a phenomenon observed in overparameterized feedforward linear networks that enables the network to achieve zero loss by fitting random noise, even on previously…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…
Motivation: Structural heterogeneity in single-particle cryo-electron microscopy (cryo-EM) data represents a major challenge for high-resolution structure determination. Unsupervised classification may serve as the first step in the…
This paper presents an algorithm for the efficient approximation of the saddle-extremum persistence diagram of a scalar field. Vidal et al. introduced recently a fast algorithm for such an approximation (by interrupting a progressive…
Likelihood-based, or explicit, deep generative models use neural networks to construct flexible high-dimensional densities. This formulation directly contradicts the manifold hypothesis, which states that observed data lies on a…