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In learning theory, a standard assumption is that the data is generated from a finite mixture model. But what happens when the number of components is not known in advance? The problem of estimating the number of components, also called…
Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…
This paper introduces a novel anomaly detection framework that combines the robust statistical principles of density-estimation-based anomaly detection methods with the representation-learning capabilities of deep learning models. The…
This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process…
This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…
This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models.…
Outlier detection in high-dimensional data is a challenging yet important task, as it has applications in, e.g., fraud detection and quality control. State-of-the-art density-based algorithms perform well because they 1) take the local…
Parton distribution functions (PDFs) form an essential part of particle physics calculations. Currently, the most precise predictions for these non-perturbative functions are generated through fits to global data. A problem that several PDF…
Traffic congestion anomaly detection is of paramount importance in intelligent traffic systems. The goals of transportation agencies are two-fold: to monitor the general traffic conditions in the area of interest and to locate road segments…
There is a growing need for machine learning-based anomaly detection strategies to broaden the search for Beyond-the-Standard-Model (BSM) physics at the Large Hadron Collider (LHC) and elsewhere. The first step of any anomaly detection…
Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…
Community detection tasks have received a lot of attention across statistics, machine learning, and information theory with a large body of work concentrating on theoretical guarantees for the stochastic block model. One line of recent work…
Affordances are fundamental descriptors of relationships between actions, objects and effects. They provide the means whereby a robot can predict effects, recognize actions, select objects and plan its behavior according to desired goals.…
A method for unsupervised contextual anomaly detection is proposed using a cross-linked pair of Variational Auto-Encoders for assigning a normality score to an observation. The method enables a distinct separation of contextual from…
Clustering mixed data presents numerous challenges inherent to the very heterogeneous nature of the variables. A clustering algorithm should be able, despite of this heterogeneity, to extract discriminant pieces of information from the…
Traffic forecasting is a challenging spatio-temporal modeling task and a critical component of urban transportation management. Current studies mainly focus on deterministic predictions, with limited considerations on the uncertainty and…
This paper proposes to use set features for detecting anomalies in samples that consist of unusual combinations of normal elements. Many leading methods discover anomalies by detecting an unusual part of a sample. For example,…
Importance sampling is a Monte Carlo technique for efficiently estimating the likelihood of rare events by biasing the sampling distribution towards the rare event of interest. By drawing weighted samples from a learned proposal…
Hyperbolic space is increasingly used for hierarchical, tree-like, and network-structured data, but likelihood-based density modeling on hyperbolic space remains relatively limited. This paper develops finite mixture modeling with isotropic…
We propose an Gaussian Mixture Model (GMM) learning algorithm, based on our previous work of GMM expansion idea. The new algorithm brings more robustness and simplicity than classic Expectation Maximization (EM) algorithm. It also improves…