Deep-embedding methods aim to discover representations of a domain that make explicit the domain's class structure and thereby support few-shot learning. Disentangling methods aim to make explicit compositional or factorial structure. We combine these two active but independent lines of research and propose a new paradigm suitable for both goals. We propose and evaluate a novel loss function based on the $F$ statistic, which describes the separation of two or more distributions. By ensuring that distinct classes are well separated on a subset of embedding dimensions, we obtain embeddings that are useful for few-shot learning. By not requiring separation on all dimensions, we encourage the discovery of disentangled representations. Our embedding method matches or beats state-of-the-art, as evaluated by performance on recall@$k$ and few-shot learning tasks. Our method also obtains performance superior to a variety of alternatives on disentangling, as evaluated by two key properties of a disentangled representation: modularity and explicitness. The goal of our work is to obtain more interpretable, manipulable, and generalizable deep representations of concepts and categories.

We present the very first robust Bayesian Online Changepoint Detection algorithm through General Bayesian Inference (GBI) with $\beta$-divergences. The resulting inference procedure is doubly robust for both the predictive and the changepoint (CP) posterior, with linear time and constant space complexity. We provide a construction for exponential models and demonstrate it on the Bayesian Linear Regression model. In so doing, we make two additional contributions: Firstly, we make GBI scalable using Structural Variational approximations that are exact as $\beta \to 0$. Secondly, we give a principled way of choosing the divergence parameter $\beta$ by minimizing expected predictive loss on-line. Reducing False Discovery Rates of \CPs from up to 99\% to 0\% on real world data, this offers the state of the art.

How great it would be if you were able to predict the number of cars your company might sell next year? How profitable you might be if you were able to predict the stock prices of a brand in advance so that you can invest without any risks? How awesome it would be if you were able to predict your salary for the next 5 years? How cool it would be if you were able to predict the score for your favourite game? All of these are possible with just one simple algorithm called Linear Regression.

Knowledge bases (KB), both automatically and manually constructed, are often incomplete --- many valid facts can be inferred from the KB by synthesizing existing information. A popular approach to KB completion is to infer new relations by combinatory reasoning over the information found along other paths connecting a pair of entities. Given the enormous size of KBs and the exponential number of paths, previous path-based models have considered only the problem of predicting a missing relation given two entities or evaluating the truth of a proposed triple. Additionally, these methods have traditionally used random paths between fixed entity pairs or more recently learned to pick paths between them. We propose a new algorithm MINERVA, which addresses the much more difficult and practical task of answering questions where the relation is known, but only one entity. Since random walks are impractical in a setting with combinatorially many destinations from a start node, we present a neural reinforcement learning approach which learns how to navigate the graph conditioned on the input query to find predictive paths. Empirically, this approach obtains state-of-the-art results on several datasets, significantly outperforming prior methods.

In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison criterion to find the optimal regularization parameters. However, we show that fixing the parameters across all folds may result in an inconsistency issue, and it is more appropriate to cross-validate projection-selection patterns to obtain the best coefficient estimate. Our in-sample error studies in jointly sparse and rank-deficient models lead to a new class of information criteria with four scale-free forms to bypass the estimation of the noise level. By use of an identity, we propose a novel scale-free calibration to help cross-validation achieve the minimax optimal error rate non-asymptotically. Experiments support the efficacy of the proposed methods.

Machine learning techniques have gained prominence for the analysis of resting-state functional Magnetic Resonance Imaging (rsfMRI) data. Here, we present an overview of various unsupervised and supervised machine learning applicationsto rsfMRI. We present a methodical taxonomy of machine learning methods in resting-state fMRI. We identify three major divisions of unsupervised learning methods with regard to their applications to rsfMRI, based on whether they discover principal modes of variation across space, time or population. Next, we survey the algorithms and rsfMRI feature representations that have driven the success of supervised subject-level predictions. Thegoal is to provide a high-level overview of the burgeoning field of rsfMRI from the perspective of machine learning applications. Keywords: Machine learning, resting-state, functional MRI, intrinsic networks, brain connectivity 1. Introduction Resting-state fMRI (rsfMRI) is a widely used neuroimaging tool that ...

K-nearest neighbor (kNN) search refers to the problem of finding K points closest toa given data point on a distance metric of interest. It is an important task in a wide range of applications, including similarity search in data mining [15,19], fast kernel methods in machine learning [17, 30, 38], nonparametric density estimation [5, 29, 31] and intrinsic dimension estimation [6, 26] in statistics, aswell as anomaly detection algorithms [2, 10, 37]. Numerous algorithms have been proposed for kNN search; the readers are referred to [35, 46] and references therein. Our interest is kNN search in emerging applications. Two 1 salient features of such applications are the expected scalability of the algorithms andtheir ability to handle data of high dimensionality. Additionally, such applications often desire more accurate kNN search. For example, robotic route planning [23] and face-based surveillance systems [34] require a high accuracy forthe robust execution of tasks. However, most existing work on kNN search [1, 4, 12, 15] have focused mainly on the fast computation and accuracy isofalessconcern.

As an only child, I spent a lot of time by myself. Oftentimes my only respite from the extreme boredom of being by myself was daydreaming. I would meditate on objects in my environment and rotate them around in my head. I now attribute my love of jigsaw puzzles, math, and art to all the time I dedicated to visualization practice. My love for those things inspired me to try and understand more about how statistical functions and K-Means Clustering are used in anomaly detection for time series data.

In a related post we discussed the Cold Start Problem in Data Science -- how do you start to build a model when you have either no training data or no clear choice of model parameters. An example of a cold start problem is k-Means Clustering, where the number of clusters k in the data set is not known in advance, and the locations of those clusters in feature space (i.e., the cluster means) are not known either. So, you start by assuming a value for k and making random assumptions about the cluster means, and then iterate until you find the optimal set of clusters, based upon some evaluation metric. See the related post for more details about the cold start challenge. See the attached graphic below for a simple demonstration of a k-Means Clustering application.

This work is concerned with the non-negative robust principal component analysis (PCA), where the goal is to recover the dominant non-negative principal component of a data matrix precisely, where a number of measurements could be grossly corrupted with sparse and arbitrary large noise. Most of the known techniques for solving the robust PCA rely on convex relaxation methods by lifting the problem to a higher dimension, which significantly increase the number of variables. As an alternative, the well-known Burer-Monteiro approach can be used to cast the robust PCA as a non-convex and non-smooth $\ell_1$ optimization problem with a significantly smaller number of variables. In this work, we show that the low-dimensional formulation of the symmetric and asymmetric positive robust PCA based on the Burer-Monteiro approach has benign landscape, i.e., 1) it does not have any spurious local solution, 2) has a unique global solution, and 3) its unique global solution coincides with the true components. An implication of this result is that simple local search algorithms are guaranteed to achieve a zero global optimality gap when directly applied to the low-dimensional formulation. Furthermore, we provide strong deterministic and statistical guarantees for the exact recovery of the true principal component. In particular, it is shown that a constant fraction of the measurements could be grossly corrupted and yet they would not create any spurious local solution.