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A major challenge when trying to detect fraud is that the fraudulent activities form a minority class which make up a very small proportion of the data set. In most data sets, fraud occurs in typically less than 0.5% of the cases. Detecting…
Despite empirical risk minimization (ERM) is widely applied in the machine learning community, its performance is limited on data with spurious correlation or subpopulation that is introduced by hidden attributes. Existing literature…
Class imbalance poses a major challenge in different classification tasks, which is a frequently occurring scenario in many real-world applications. Data resampling is considered to be the standard approach to address this issue. The goal…
Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…
The training of deep neural networks is inherently a nonconvex optimization problem, yet standard approaches such as stochastic gradient descent (SGD) require simultaneous updates to all parameters, often leading to unstable convergence and…
Stochastic Neighbor Embedding (SNE) methods minimize the divergence between the similarity matrix of a high-dimensional data set and its counterpart from a low-dimensional embedding, leading to widely applied tools for data visualization.…
Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and…
Metropolis nested sampling evolves a Markov chain from a current livepoint and accepts new points along the chain according to a version of the Metropolis acceptance ratio modified to satisfy the likelihood constraint, characteristic of…
For optimization on large-scale data, exactly calculating its solution may be computationally difficulty because of the large size of the data. In this paper we consider subsampled optimization for fast approximating the exact solution. In…
Learning from set-structured data is a fundamental problem that has recently attracted increasing attention, where a series of summary networks are introduced to deal with the set input. In fact, many meta-learning problems can be treated…
We present a framework for smooth optimization of explicitly regularized objectives for (structured) sparsity. These non-smooth and possibly non-convex problems typically rely on solvers tailored to specific models and regularizers. In…
The Morse-Smale complex is a standard tool in visual data analysis. The classic definition is based on a continuous view of the gradient of a scalar function where its zeros are the critical points. These points are connected via gradient…
We consider unconstrained multi-criteria optimization problems with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust region framework where additional sampling approach is used to govern the sample size…
We propose Score-of-Mixture Training (SMT), a novel framework for training one-step generative models by minimizing a class of divergences called the $\alpha$-skew Jensen--Shannon divergence. At its core, SMT estimates the score of mixture…
In many situations, sample data is obtained from a noisy or imperfect source. In order to address such corruptions, this paper introduces the concept of a sampling corrector. Such algorithms use structure that the distribution is purported…
Sampling without replacement is a natural online rounding strategy for converting fractional bipartite matching into an integral one. In Online Bipartite Matching, we can use the Balance algorithm to fractionally match each online vertex,…
We study distribution-free property testing and learning problems where the unknown probability distribution is a product distribution over $\mathbb{R}^d$. For many important classes of functions, such as intersections of halfspaces,…
This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby…
Nested sampling is an iterative integration procedure that shrinks the prior volume towards higher likelihoods by removing a "live" point at a time. A replacement point is drawn uniformly from the prior above an ever-increasing likelihood…
In traditional models of supervised learning, the goal of a learner -- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$ -- is to output a hypothesis that is competitive (to within $\epsilon$) of the…