Non-negative matrix factorization (NMF) minimizes the Euclidean distance between the data matrix and its low rank approximation, and it fails when applied to corrupted data because the loss function is sensitive to outliers. In this paper, we propose a Truncated CauchyNMF loss that handle outliers by truncating large errors, and develop a Truncated CauchyNMF to robustly learn the subspace on noisy datasets contaminated by outliers. We theoretically analyze the robustness of Truncated CauchyNMF comparing with the competing models and theoretically prove that Truncated CauchyNMF has a generalization bound which converges at a rate of order $O(\sqrt{{\ln n}/{n}})$, where $n$ is the sample size. We evaluate Truncated CauchyNMF by image clustering on both simulated and real datasets. The experimental results on the datasets containing gross corruptions validate the effectiveness and robustness of Truncated CauchyNMF for learning robust subspaces.

Recent results in Reinforcement Learning (RL) have shown that agents with limited training environments are susceptible to a large amount of overfitting across many domains. A key challenge for RL generalization is to quantitatively explain the effects of changing parameters on testing performance. Such parameters include architecture, regularization, and RL-dependent variables such as discount factor and action stochasticity. We provide empirical results that show complex and interdependent relationships between hyperparameters and generalization. We further show that several empirical metrics such as gradient cosine similarity and trajectory-dependent metrics serve to provide intuition towards these results.

Inverse reinforcement learning (IRL) enables an agent to learn complex behavior by observing demonstrations from a (near-)optimal policy. The typical assumption is that the learner's goal is to match the teacher's demonstrated behavior. In this paper, we consider the setting where the learner has her own preferences that she additionally takes into consideration. These preferences can for example capture behavioral biases, mismatched worldviews, or physical constraints. We study two teaching approaches: learner-agnostic teaching, where the teacher provides demonstrations from an optimal policy ignoring the learner's preferences, and learner-aware teaching, where the teacher accounts for the learner's preferences. We design learner-aware teaching algorithms and show that significant performance improvements can be achieved over learner-agnostic teaching.

Requirements No Such Pre-req, its good to have some basic math concepts Description Data Science is a multidisciplinary field that deals with the study of data. Data scientists have the ability to take data, understand it, process it, and extract information from it, visualize the information and communicate it. Data scientists are well-versed in multiple disciplines including mathematics, statistics, economics, business, and computer science, as well as the unique ability to ask interesting and challenging data questions based on formal or informal theory to spawn valuable and meticulous insights. This course introduces students to this rapidly growing field and equips them with its most fundamental principles, tools, and mindset. Have an in-depth understanding of the concepts of Machine Learning Be able to grasp, understand, and write machine learning code from scratch Use Builtin Libraries available to build machine learning models Be able to analyze, build, and assess models on any dataset Be able to interpret and understand the black box behind model Understand the applications of data science by exhibiting the ability to work on different datasets and interpreting them.

Earlier this month Google quietly unveiled an incredibly unique opportunity for seasoned developers to explore pilot experiments based on some of Google's frontier AI research, aptly called "AI Workshop." Google already makes a wealth of AI research available on platforms from GitHub to its own AI Hub, complete with a searchable library of ready-to-use code examples, demonstrations and even wrappers around production systems. What makes AI Workshop so different from these other mediums is that it presents an early glimpse at selections from Google's bleeding edge enterprise AI research that might become future product offerings, allowing the research and developer community to provide feedback that can help influence those innovations, granting a rare opportunity to help shape the future of AI in the enterprise. The rise of deep learning has represented a unique era of collaboration between the commercial and research sectors. Many of the underlying toolkits, workflows, algorithms and even research models have all been released under open source licenses, with companies, academics and citizen researchers collaborating together to create innovative new applications and to improve the underlying infrastructure powering the modern deep learning revolution.

More than 80 percent of the world's oceans are currently unmapped, but a $7 million prize pool to explore the deep sea hopes to change that. The Ocean Discovery XPrize was today awarded to teams using uncrewed deep-sea vehicles to map the ocean floor and trace chemical signals underwater. The goal is to develop a comprehensive atlas by 2030. The grand prize required entrants to develop an autonomous vessel capable of mapping at least 250 square kilometres of the sea floor within 24 hours, up to a depth of 4 kilometres below surface level. The maps must be fairly high resolution, with data points taken no more than five metres apart.

This tutorial explains Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) as two fundamental classification methods in statistical and probabilistic learning. We start with the optimization of decision boundary on which the posteriors are equal. Then, LDA and QDA are derived for binary and multiple classes. The estimation of parameters in LDA and QDA are also covered. Then, we explain how LDA and QDA are related to metric learning, kernel principal component analysis, Mahalanobis distance, logistic regression, Bayes optimal classifier, Gaussian naive Bayes, and likelihood ratio test. We also prove that LDA and Fisher discriminant analysis are equivalent. We finally clarify some of the theoretical concepts with simulations we provide.

As application demands for online convex optimization accelerate, the need for designing new methods that simultaneously cover a large class of convex functions and impose the lowest possible regret is highly rising. Known online optimization methods usually perform well only in specific settings, and their performance depends highly on the geometry of the decision space and cost functions. However, in practice, lack of such geometric information leads to confusion in using the appropriate algorithm. To address this issue, some adaptive methods have been proposed that focus on adaptively learning parameters such as step size, Lipschitz constant, and strong convexity coefficient, or on specific parametric families such as quadratic regularizers. In this work, we generalize these methods and propose a framework that competes with the best algorithm in a family of expert algorithms. Our framework includes many of the well-known adaptive methods including MetaGrad, MetaGrad+C, and Ader. We also introduce a second algorithm that computationally outperforms our first algorithm with at most a constant factor increase in regret. Finally, as a representative application of our proposed algorithm, we study the problem of learning the best regularizer from a family of regularizers for Online Mirror Descent. Empirically, we support our theoretical findings in the problem of learning the best regularizer on the simplex and $l_2$-ball in a multiclass learning problem.

Non-stationarity appears in many online applications such as web search and advertising. In this paper, we study the online learning to rank problem in a non-stationary environment where user preferences change abruptly at an unknown moment in time. We consider the problem of identifying the K most attractive items and propose cascading non-stationary bandits, an online learning variant of the cascading model, where a user browses a ranked list from top to bottom and clicks on the first attractive item. We propose two algorithms for solving this non-stationary problem: CascadeDUCB and CascadeSWUCB. We analyze their performance and derive gap-dependent upper bounds on the n-step regret of these algorithms. We also establish a lower bound on the regret for cascading non-stationary bandits and show that both algorithms match the lower bound up to a logarithmic factor. Finally, we evaluate their performance on a real-world web search click dataset.

There have been different strategies to improve the performance of a machine learning model, e.g., increasing the depth, width, and/or nonlinearity of the model, and using ensemble learning to aggregate multiple base/weak learners in parallel or in series. This paper proposes a novel strategy called patch learning (PL) for this problem. It consists of three steps: 1) train an initial global model using all training data; 2) identify from the initial global model the patches which contribute the most to the learning error, and train a (local) patch model for each such patch; and, 3) update the global model using training data that do not fall into any patch. To use a PL model, we first determine if the input falls into any patch. If yes, then the corresponding patch model is used to compute the output. Otherwise, the global model is used. We explain in detail how PL can be implemented using fuzzy systems. Five regression problems on 1D/2D/3D curve fitting, nonlinear system identification, and chaotic time-series prediction, verified its effectiveness. To our knowledge, the PL idea has not appeared in the literature before, and it opens up a promising new line of research in machine learning.