We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and redundancy principles. By two different interpretations (exploiting properties of power series of matrices and relying on Markov chains fundamentals) we can evaluate the values of paths (i.e., feature subsets) of arbitrary lengths, eventually go to infinite, from which we dub our framework Infinite Feature Selection (Inf-FS). Going to infinite allows to constrain the computational complexity of the selection process, and to rank the features in an elegant way, that is, considering the value of any path (subset) containing a particular feature. We also propose a simple unsupervised strategy to cut the ranking, so providing the subset of features to keep. In the experiments, we analyze diverse settings with heterogeneous features, for a total of 11 benchmarks, comparing against 18 widely-known comparative approaches. The results show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori, or when the decision of the subset cardinality is part of the process.

We address the problem of unsupervised domain adaptation under the setting of generalized target shift (both class-conditional and label shifts occur). We show that in that setting, for good generalization, it is necessary to learn with similar source and target label distributions and to match the class-conditional probabilities. For this purpose, we propose an estimation of target label proportion by blending mixture estimation and optimal transport. This estimation comes with theoretical guarantees of correctness. Based on the estimation, we learn a model by minimizing a importance weighted loss and a Wasserstein distance between weighted marginals. We prove that this minimization allows to match class-conditionals given mild assumptions on their geometry. Our experimental results show that our method performs better on average than competitors accross a range domain adaptation problems including digits,VisDA and Office.

The systematic minimization of the quantifiable uncertainty, or risk [22], is one of the core objectives in all disciplines involving decision-making, e.g., economics and finance. Within machine learning contexts, strategies for risk-aversion have been most actively studied under sequential decision-making and reinforcement learning frameworks [21, 8], giving birth to a number of algorithms based on Markov decision processes (MDPs) and multi-armed bandits. In those works, various risk-averse measures of loss have been used as a minimization objective, instead of the risk-neutral expected loss; popular risk measures include entropic risk [21, 6, 7], mean-variance [39, 13, 28], and a slightly more modern alternative known as conditional value-at-risk (CVaR [15, 10, 42]). Yet, with growing interest to the societal impacts of machine intelligence, the importance of risk-aversion under non-sequential scenarios has also been spotlighted recently. For instance, Williamson and Menon [45] give an axiomatic characterization of the fairness risk measures, and propose a convex fairness-aware objective based on CVaR.

Clustering and prediction are two primary tasks in the fields of unsupervised and supervised learning, respectively. Although much of the recent advances in machine learning have been centered around those two tasks, the interdependent, mutually beneficial relationship between them is rarely explored. One could reasonably expect appropriately clustering the data would aid the downstream prediction task and, conversely, a better prediction performance for the downstream task could potentially inform a more appropriate clustering strategy. In this work, we focus on the latter part of this mutually beneficial relationship. To this end, we introduce Deep Goal-Oriented Clustering (DGC), a probabilistic framework that clusters the data by jointly using supervision via side-information and unsupervised modeling of the inherent data structure in an end-to-end fashion. We show the effectiveness of our model on a range of datasets by achieving prediction accuracies comparable to the state-of-the-art, while, more importantly in our setting, simultaneously learning congruent clustering strategies.

This paper analyzes the convergence for a large class of Riemannian stochastic approximation (SA) schemes, which aim at tackling stochastic optimization problems. In particular, the recursions we study use either the exponential map of the considered manifold (geodesic schemes) or more general retraction functions (retraction schemes) used as a proxy for the exponential map. Such approximations are of great interest since they are low complexity alternatives to geodesic schemes. Under the assumption that the mean field of the SA is correlated with the gradient of a smooth Lyapunov function (possibly non-convex), we show that the above Riemannian SA schemes find an ${\mathcal{O}}(b_\infty + \log n / \sqrt{n})$-stationary point (in expectation) within ${\mathcal{O}}(n)$ iterations, where $b_\infty \geq 0$ is the asymptotic bias. Compared to previous works, the conditions we derive are considerably milder. First, all our analysis are global as we do not assume iterates to be a-priori bounded. Second, we study biased SA schemes. To be more specific, we consider the case where the mean-field function can only be estimated up to a small bias, and/or the case in which the samples are drawn from a controlled Markov chain. Third, the conditions on retractions required to ensure convergence of the related SA schemes are weak and hold for well-known examples. We illustrate our results on three machine learning problems.

Machine learning (ML) is rapidly changing the world, from diverse types of applications and research pursued in industry and academia. Machine learning is affecting every part of our daily lives. From voice assistants using NLP and machine learning to make appointments, check our calendar and play music, to programmatic advertisements -- that are so accurate that they can predict what we will need before we even think of it. More often than not, the complexity of the scientific field of machine learning can be overwhelming, making keeping up with "what is important" a very challenging task. However, to make sure that we provide a learning path to those who seek to learn machine learning, but are new to these concepts.

This article requires the knowledge of Linear Regression. If you haven't heard of it, then please check out an article on Linear Regression before you proceed here. Till now we assumed that the relationship between independent variable X and dependent Y can be represented with a straight line. But what if when we can't represent the relationship in a straight line because the data might not be linearly separable? In such kind of scenario we can look for polynomial regression.

UC Berkeley AI researchers are using an iPhone X and Apple's ARKit to train a robotic arm how to grasp an object. ARKit creates point clouds from data generated by moving an RGB camera around an object for two minutes. Robotic grasping is a particular robotics subfield focused on the challenge of teaching a robot to pick up, move, manipulate, or grasp an object. The Dexterity Network, or Dex-Net, research project at UC Berkeley's Autolab dates back to 2017 and includes open source training data sets and pretrained models for robotic grasping in an ecommerce bin-picking scenario. The ability for robots to quickly learn how to grasp objects has a big impact on how automated warehouses like Amazon fulfillment centers can become.

In this post, we will see a simple and intuitive explanation of Boosting algorithms: what they are, why they are so powerful, some of the different types, and how they are trained and used to make predictions. We will avoid all the heavy maths and go for a clear, simple, but in depth explanation that can be easily understood. However, additional material and resources will be left at the end of the post, in case you want to dive further into the topic. Traditionally, building a Machine Learning application consisted on taking a single learner, like a Logistic Regressor, a Decision Tree, Support Vector Machine, or an Artificial Neural Network, feeding it data, and teaching it to perform a certain task through this data. Then ensemble methods were born, which involve using many learners to enhance the performance of any single one of them individually.

Welcome to the first installment in our Deep Learning Experiments series, where we run experiments to evaluate commonly-held assumptions about training neural networks. Our goal is to better understand the different design choices that affect model training and evaluation. To do so, we come up with questions about each design choice and then run experiments to answer them. In this article, we seek to better understand the impact of batch size on training neural networks. Typically, this is done using gradient descent, which computes the gradient of the loss function with respect to the parameters, and takes a step in that direction.