Related papers: Robust Model Selection and Nearly-Proper Learning …
The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major…
Assuming an exponential power distribution is one way to deal with outliers in regression and clustering, which can increase the robustness of the analysis. Gaussian distribution is a special case of an exponential distribution. And an…
Data pruning -- the combinatorial task of selecting a small and representative subset from a large dataset, is crucial for mitigating the enormous computational costs associated with training data-hungry modern deep learning models at…
Mixture modelling using elliptical distributions promises enhanced robustness, flexibility and stability over the widely employed Gaussian mixture model (GMM). However, existing studies based on the elliptical mixture model (EMM) are…
We study the problem of learning a distribution from samples, when the underlying distribution is a mixture of product distributions over discrete domains. This problem is motivated by several practical applications such as crowd-sourcing,…
Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling…
We study the problem of list-decodable Gaussian mean estimation and the related problem of learning mixtures of separated spherical Gaussians. We develop a set of techniques that yield new efficient algorithms with significantly improved…
Variational inference with Gaussian mixture models (GMMs) enables learning of highly tractable yet multi-modal approximations of intractable target distributions with up to a few hundred dimensions. The two currently most effective methods…
This paper investigates model robustness in reinforcement learning (RL) to reduce the sim-to-real gap in practice. We adopt the framework of distributionally robust Markov decision processes (RMDPs), aimed at learning a policy that…
We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…
Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. We propose a "compressive learning" framework where we estimate model parameters from a sketch of the training data. This sketch…
We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers. While strong guarantees are available when the outlier fraction is significantly smaller than the minimum mixing weight,…
A $k$-modal probability distribution over the discrete domain $\{1,...,n\}$ is one whose histogram has at most $k$ "peaks" and "valleys." Such distributions are natural generalizations of monotone ($k=0$) and unimodal ($k=1$) probability…
We consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. In the most basic form of this problem, we are given samples from a uniform mixture of…
The recent emergence of deep learning has led to a great deal of work on designing supervised deep semantic segmentation algorithms. As in many tasks sufficient pixel-level labels are very difficult to obtain, we propose a method which…
Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…
We introduce an unsupervised clustering algorithm to improve training efficiency and accuracy in predicting energies using molecular-orbital-based machine learning (MOB-ML). This work determines clusters via the Gaussian mixture model (GMM)…
We propose a novel data-driven method to learn a mixture of multiple kernels with random features that is certifiabaly robust against adverserial inputs. Specifically, we consider a distributionally robust optimization of the kernel-target…
We study the gradient Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM) in the over-parameterized setting, where a general GMM with $n>1$ components learns from data that are generated by a single ground truth…
A common assumption in machine learning is that samples are independently and identically distributed (i.i.d). However, the contributions of different samples are not identical in training. Some samples are difficult to learn and some…