Related papers: Source Identification for Mixtures of Product Dist…
We give under weak assumptions a complete combinatorial characterization of identifiability for linear mixtures of finite alphabet sources, with unknown mixing weights and unknown source signals, but known alphabet. This is based on a…
This article discusses the problem of estimation of parameters in finite mixtures when the mixture components are assumed to be symmetric and to come from the same location family. We refer to these mixtures as semi-parametric because no…
We consider the problem of identifying, from statistics, a distribution of discrete random variables $X_1,\ldots,X_n$ that is a mixture of $k$ product distributions. The best previous sample complexity for $n \in O(k)$ was $(1/\zeta)^{O(k^2…
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…
We study the problem of learning a mixture model of non-parametric product distributions. The problem of learning a mixture model is that of finding the component distributions along with the mixing weights using observed samples generated…
We give an algorithm for learning a mixture of {\em unstructured} distributions. This problem arises in various unsupervised learning scenarios, for example in learning {\em topic models} from a corpus of documents spanning several topics.…
Estimation of the number of sources in a linear mixture is a critical preprocessing step in the separation and analysis of the sources for many applications. Historically, statistical methods, such as the minimum description length and…
We introduce the problem of learning mixtures of $k$ subcubes over $\{0,1\}^n$, which contains many classic learning theory problems as a special case (and is itself a special case of others). We give a surprising $n^{O(\log k)}$-time…
We consider the problem of identifying, from its first $m$ noisy moments, a probability distribution on $[0,1]$ of support $k<\infty$. This is equivalent to the problem of learning a distribution on $m$ observable binary random variables…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
In the context of PDE-constrained optimization theory, source identification problems traditionally entail particles emerging from an unknown source distribution inside a domain, moving according to a prescribed stochastic process,…
The problem of identifiability of finite mixtures of finite product measures is studied. A mixture model with $K$ mixture components and $L$ observed variables is considered, where each variable takes its value in a finite set with…
The method of moments is a classical statistical technique for density estimation that solves a system of moment equations to estimate the parameters of an unknown distribution. A fundamental question critical to understanding…
Factor analysis is broadly used as a powerful unsupervised machine learning tool for reconstruction of hidden features in recorded mixtures of signals. In the case of a linear approximation, the mixtures can be decomposed by a variety of…
This paper proposes a determined blind source separation method using Bayesian non-parametric modelling of sources. Conventionally source signals are separated from a given set of mixture signals by modelling them using non-negative matrix…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
Recent work has shown that finite mixture models with $m$ components are identifiable, while making no assumptions on the mixture components, so long as one has access to groups of samples of size $2m-1$ which are known to come from the…
The inverse source problem where an unknown source is to be identified from the knowledge of its radiated wave is studied. The focus is placed on the effect that multi-frequency data has on establishing uniqueness. In particular, it is…
We study the inference of the origin and the pattern of contamination in water distribution networks. We assume a simplified model for the dyanmics of the contamination spread inside a water distribution network, and assume that at some…
The inverse problem of recovering point sources represents an important class of applied inverse problems. However, there is still a lack of neural network-based methods for point source identification, mainly due to the inherent solution…