Geodesic distance is the shortest path between two points in a Riemannian manifold. Manifold learning algorithms, such as Isomap, seek to learn a manifold that preserves geodesic distances. However, such methods operate on the ambient dimensionality, and are therefore fragile to noise dimensions. We developed an unsupervised random forest method (URerF) to approximately learn geodesic distances in linear and nonlinear manifolds with noise. URerF operates on low-dimensional sparse linear combinations of features, rather than the full observed dimensionality. To choose the optimal split in a computationally efficient fashion, we developed a fast Bayesian Information Criterion statistic for Gaussian mixture models. We introduce geodesic precision-recall curves which quantify performance relative to the true latent manifold. Empirical results on simulated and real data demonstrate that URerF is robust to high-dimensional noise, where as other methods, such as Isomap, UMAP, and FLANN, quickly deteriorate in such settings. In particular, URerF is able to estimate geodesic distances on a real connectome dataset better than other approaches.

We propose networkmetrics, a new data-driven approach for monitoring, troubleshooting and understanding communication networks using multivariate analysis. Networkmetric models are powerful machine-learning tools to interpret and interact with data collected from a network. In this paper, we illustrate the application of Multivariate Big Data Analysis (MBDA), a recently proposed networkmetric method with application to Big Data sets. We use MBDA for the detection and troubleshooting of network problems in a campus-wide Wi-Fi network. Data includes a seven-year trace (from 2012 to 2018) of the network's most recent activity, with approximately 3,000 distinct access points, 40,000 authenticated users, and 600,000 distinct Wi-Fi stations. This is the longest and largest Wi-Fi trace known to date. To analyze this data, we propose learning and visualization procedures that extend MBDA. These procedures result in a methodology that allows network analysts to identify problems and diagnose and troubleshoot them, optimizing the network performance. In the paper, we go through the entire workflow of the approach, illustrating its application in detail and discussing processing times for parallel hardware.

Imitation Learning (IL) is a machine learning approach to learn a policy from a dataset of demonstrations. IL can be useful to kick-start learning before applying reinforcement learning (RL) but it can also be useful on its own, e.g. to learn to imitate human players in video games. However, a major limitation of current IL approaches is that they learn only a single "average" policy based on a dataset that possibly contains demonstrations of numerous different types of behaviors. In this paper, we propose a new approach called Behavioral Repertoire Imitation Learning (BRIL) that instead learns a repertoire of behaviors from a set of demonstrations by augmenting the state-action pairs with behavioral descriptions. The outcome of this approach is a single neural network policy conditioned on a behavior description that can be precisely modulated. We apply this approach to train a policy on 7,777 human replays to perform build-order planning in StarCraft II. Principal Component Analysis (PCA) is applied to construct a low-dimensional behavioral space from the high-dimensional army unit composition of each demonstration. The results demonstrate that the learned policy can be effectively manipulated to express distinct behaviors. Additionally, by applying the UCB1 algorithm, we are able to adapt the behavior of the policy - in-between games - to reach a performance beyond that of the traditional IL baseline approach.

We introduce Invariant Risk Minimization (IRM), a learning paradigm to estimate invariant correlations across multiple training distributions. To achieve this goal, IRM learns a data representation such that the optimal classifier, on top of that data representation, matches for all training distributions. Through theory and experiments, we show how the invariances learned by IRM relate to the causal structures governing the data and enable out-of-distribution generalization.

Pixel intensity is a widely used feature for clustering and segmentation algorithms, the resulting segmentation using only intensity values might suffer from noises and lack of spatial context information. Wavelet transform is often used for image denoising and classification. We proposed a novel method to incorporate Wavelet features in segmentation and clustering algorithms. The conventional K-means, Fuzzy c-means (FCM), and Active contour without edges (ACWE) algorithms were modified to adapt Wavelet features, leading to robust clustering/segmentation algorithms. A weighting parameter to control the weight of low-frequency sub-band information was also introduced. The new algorithms showed the capability to converge to different segmentation results based on the frequency information derived from the Wavelet sub-bands.

Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically unfounded, such as searching for an elbow in the curve of a given cost measure. In contrast, statistically founded methods often make strict assumptions over the data distribution or come with their own optimization scheme for the clustering objective. This limits either the set of applicable datasets or clustering algorithms. In this paper, we strive to determine the number of clusters by answering a simple question: given two clusters, is it likely that they jointly stem from a single distribution? To this end, we propose a bound on the probability that two clusters originate from the distribution of the unified cluster, specified only by the sample mean and variance. Our method is applicable as a simple wrapper to the result of any clustering method minimizing the objective of $k$-means, which includes Gaussian mixtures and Spectral Clustering. We focus in our experimental evaluation on an application for nonconvex clustering and demonstrate the suitability of our theoretical results. Our \textsc{SpecialK} clustering algorithm automatically determines the appropriate value for $k$, without requiring any data transformation or projection, and without assumptions on the data distribution. Additionally, it is capable to decide that the data consists of only a single cluster, which many existing algorithms cannot.

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications, including long-term asymptotic patterns. Whereas state-of-the-art data-driven approaches rely on delay embeddings and linear decompositions of the underlying operators, we introduce a framework based on the data-driven identification of an augmented state-space model using a neural-network-based representation. For a given training dataset, it amounts to jointly learn an ODE (Ordinary Differential Equation) representation in the latent space and reconstructing latent states. Through numerical experiments, we demonstrate the relevance of the proposed framework w.r.t. state-of-the-art approaches in terms of short-term forecasting performance and long-term behaviour. We further discuss how the proposed framework relates to Koopman operator theory and Takens' embedding theorem.

In recent years, there have been significant efforts on mitigating unethical demographic biases in machine learning methods. However, very little is done for kernel methods. In this paper, we propose a new fair kernel regression method via fair feature embedding (FKR-F$^2$E) in kernel space. Motivated by prior works on feature selection in kernel space and feature processing for fair machine learning, we propose to learn fair feature embedding functions that minimize demographic discrepancy of feature distributions in kernel space. Compared to the state-of-the-art fair kernel regression method and several baseline methods, we show FKR-F$^2$E achieves significantly lower prediction disparity across three real-world data sets.

We design a new algorithm for the Euclidean $k$-means problem that operates in the local model of differential privacy. Unlike in the non-private literature, differentially private algorithms for the $k$-means incur both additive and multiplicative errors. Our algorithm significantly reduces the additive error while keeping the multiplicative error the same as in previous state-of-the-art results. Specifically, on a database of size $n$, our algorithm guarantees $O(1)$ multiplicative error and $\approx n^{1/2+a}$ additive error for an arbitrarily small constant $a$, whereas all previous algorithms in the local model on had additive error $\approx n^{2/3+a}$. We give a simple lower bound showing that additive error of $\approx\sqrt{n}$ is necessary for $k$-means algorithms in the local model (at least for algorithms with a constant number of interaction rounds, which is the setting we consider in this paper).

With the recent advances in complex networks theory, graph-based techniques for image segmentation has attracted great attention recently. In order to segment the image into meaningful connected components, this paper proposes an image segmentation general framework using complex networks based community detection algorithms. If we consider regions as communities, using community detection algorithms directly can lead to an over-segmented image. To address this problem, we start by splitting the image into small regions using an initial segmentation. The obtained regions are used for building the complex network. To produce meaningful connected components and detect homogeneous communities, some combinations of color and texture based features are employed in order to quantify the regions similarities. To sum up, the network of regions is constructed adaptively to avoid many small regions in the image, and then, community detection algorithms are applied on the resulting adaptive similarity matrix to obtain the final segmented image. Experiments are conducted on Berkeley Segmentation Dataset and four of the most influential community detection algorithms are tested. Experimental results have shown that the proposed general framework increases the segmentation performances compared to some existing methods.