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9 Completely Free Statistics Courses for Data Science

#artificialintelligence

This is a complete Free course for statistics. In this course, you will learn how to estimate parameters of a population using sample statistics, hypothesis testing and confidence intervals, t-tests and ANOVA, correlation and regression, and chi-squared test. This course is taught by industry professionals and you will learn by doing various exercises.


The Application of Machine Learning Techniques for Predicting Match Results in Team Sport: A Review

Journal of Artificial Intelligence Research

Predicting the results of matches in sport is a challenging and interesting task. In this paper, we review a selection of studies from 1996 to 2019 that used machine learning for predicting match results in team sport. Considering both invasion sports and striking/fielding sports, we discuss commonly applied machine learning algorithms, as well as common approaches related to data and evaluation. Our study considers accuracies that have been achieved across different sports, and explores whether evidence exists to support the notion that outcomes of some sports may be inherently more difficult to predict. We also uncover common themes of future research directions and propose recommendations for future researchers. Although there remains a lack of benchmark datasets (apart from in soccer), and the differences between sports, datasets and features makes between-study comparisons difficult, as we discuss, it is possible to evaluate accuracy performance in other ways. Artificial Neural Networks were commonly applied in early studies, however, our findings suggest that a range of models should instead be compared. Selecting and engineering an appropriate feature set appears to be more important than having a large number of instances. For feature selection, we see potential for greater inter-disciplinary collaboration between sport performance analysis, a sub-discipline of sport science, and machine learning.


A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

arXiv.org Machine Learning

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional $\mathcal{O}(10^{\ge 2})$ stochastic inputs (e.g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges. The curse of dimensionality can be addressed with suitable unsupervised learning techniques used as a pre-processing tool to encode inputs onto lower-dimensional subspaces while retaining its structural information and meaningful properties. In this work, we review and investigate thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods and utilize the resulting embeddings to construct a mapping to quantities of interest via polynomial chaos expansions (PCE). We refer to the general proposed approach as manifold PCE (m-PCE), where manifold corresponds to the latent space resulting from any of the studied dimension reduction methods. To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying complexity modeled as both Gaussian and non-Gaussian random fields to investigate the effect of the intrinsic dimensionality of input data. We demonstrate both the advantages and limitations of the unsupervised learning methods and we conclude that a suitable m-PCE model provides a cost-effective approach compared to alternative algorithms proposed in the literature, including recently proposed expensive deep neural network-based surrogates and can be readily applied for high-dimensional UQ in stochastic PDEs.


Impact of Parameter Sparsity on Stochastic Gradient MCMC Methods for Bayesian Deep Learning

arXiv.org Artificial Intelligence

Bayesian methods hold significant promise for improving the uncertainty quantification ability and robustness of deep neural network models. Recent research has seen the investigation of a number of approximate Bayesian inference methods for deep neural networks, building on both the variational Bayesian and Markov chain Monte Carlo (MCMC) frameworks. A fundamental issue with MCMC methods is that the improvements they enable are obtained at the expense of increased computation time and model storage costs. In this paper, we investigate the potential of sparse network structures to flexibly trade-off model storage costs and inference run time against predictive performance and uncertainty quantification ability. We use stochastic gradient MCMC methods as the core Bayesian inference method and consider a variety of approaches for selecting sparse network structures. Surprisingly, our results show that certain classes of randomly selected substructures can perform as well as substructures derived from state-of-the-art iterative pruning methods while drastically reducing model training times.


Tutorial on amortized optimization for learning to optimize over continuous domains

arXiv.org Artificial Intelligence

Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use learning to predict the solutions to problems in these settings. This leverages the shared structure between similar problem instances. In this tutorial, we will discuss the key design choices behind amortized optimization, roughly categorizing 1) models into fully-amortized and semi-amortized approaches, and 2) learning methods into regression-based and objectivebased. We then view existing applications through these foundations to draw connections between them, including for manifold optimization, variational inference, sparse coding, meta-learning, control, reinforcement learning, convex optimization, and deep equilibrium networks. This framing enables us easily see, for example, that the amortized inference in variational autoencoders is conceptually identical to value gradients in control and reinforcement learning as they both use fully-amortized models with an objective-based loss.


Towards a Theoretical Understanding of Word and Relation Representation

arXiv.org Machine Learning

Representing words by vectors, or embeddings, enables computational reasoning and is foundational to automating natural language tasks. For example, if word embeddings of similar words contain similar values, word similarity can be readily assessed, whereas judging that from their spelling is often impossible (e.g. cat /feline) and to predetermine and store similarities between all words is prohibitively time-consuming, memory intensive and subjective. We focus on word embeddings learned from text corpora and knowledge graphs. Several well-known algorithms learn word embeddings from text on an unsupervised basis by learning to predict those words that occur around each word, e.g. word2vec and GloVe. Parameters of such word embeddings are known to reflect word co-occurrence statistics, but how they capture semantic meaning has been unclear. Knowledge graph representation models learn representations both of entities (words, people, places, etc.) and relations between them, typically by training a model to predict known facts in a supervised manner. Despite steady improvements in fact prediction accuracy, little is understood of the latent structure that enables this. The limited understanding of how latent semantic structure is encoded in the geometry of word embeddings and knowledge graph representations makes a principled means of improving their performance, reliability or interpretability unclear. To address this: 1. we theoretically justify the empirical observation that particular geometric relationships between word embeddings learned by algorithms such as word2vec and GloVe correspond to semantic relations between words; and 2. we extend this correspondence between semantics and geometry to the entities and relations of knowledge graphs, providing a model for the latent structure of knowledge graph representation linked to that of word embeddings.


Submodularity In Machine Learning and Artificial Intelligence

arXiv.org Artificial Intelligence

In this manuscript, we offer a gentle review of submodularity and supermodularity and their properties. We offer a plethora of submodular definitions; a full description of a number of example submodular functions and their generalizations; example discrete constraints; a discussion of basic algorithms for maximization, minimization, and other operations; a brief overview of continuous submodular extensions; and some historical applications. We then turn to how submodularity is useful in machine learning and artificial intelligence. This includes summarization, and we offer a complete account of the differences between and commonalities amongst sketching, coresets, extractive and abstractive summarization in NLP, data distillation and condensation, and data subset selection and feature selection. We discuss a variety of ways to produce a submodular function useful for machine learning, including heuristic hand-crafting, learning or approximately learning a submodular function or aspects thereof, and some advantages of the use of a submodular function as a coreset producer. We discuss submodular combinatorial information functions, and how submodularity is useful for clustering, data partitioning, parallel machine learning, active and semi-supervised learning, probabilistic modeling, and structured norms and loss functions.


Robust Imitation Learning from Corrupted Demonstrations

arXiv.org Machine Learning

We consider offline Imitation Learning from corrupted demonstrations where a constant fraction of data can be noise or even arbitrary outliers. Classical approaches such as Behavior Cloning assumes that demonstrations are collected by an presumably optimal expert, hence may fail drastically when learning from corrupted demonstrations. We propose a novel robust algorithm by minimizing a Median-of-Means (MOM) objective which guarantees the accurate estimation of policy, even in the presence of constant fraction of outliers. Our theoretical analysis shows that our robust method in the corrupted setting enjoys nearly the same error scaling and sample complexity guarantees as the classical Behavior Cloning in the expert demonstration setting. Our experiments on continuous-control benchmarks validate that our method exhibits the predicted robustness and effectiveness, and achieves competitive results compared to existing imitation learning methods.


Probability estimation and structured output prediction for learning preferences in last mile delivery

arXiv.org Artificial Intelligence

We study the problem of learning the preferences of drivers and planners in the context of last mile delivery. Given a data set containing historical decisions and delivery locations, the goal is to capture the implicit preferences of the decision-makers. We consider two ways to use the historical data: one is through a probability estimation method that learns transition probabilities between stops (or zones). This is a fast and accurate method, recently studied in a VRP setting. Furthermore, we explore the use of machine learning to infer how to best balance multiple objectives such as distance, probability and penalties. Specifically, we cast the learning problem as a structured output prediction problem, where training is done by repeatedly calling the TSP solver. Another important aspect we consider is that for last-mile delivery, every address is a potential client and hence the data is very sparse. Hence, we propose a two-stage approach that first learns preferences at the zone level in order to compute a zone routing; after which a penalty-based TSP computes the stop routing. Results show that the zone transition probability estimation performs well, and that the structured output prediction learning can improve the results further. We hence showcase a successful combination of both probability estimation and machine learning, all the while using standard TSP solvers, both during learning and to compute the final solution; this means the methodology is applicable to other, real-life, TSP variants, or proprietary solvers.


Towards holistic scene understanding: Semantic segmentation and beyond

arXiv.org Artificial Intelligence

This dissertation addresses visual scene understanding and enhances segmentation performance and generalization, training efficiency of networks, and holistic understanding. First, we investigate semantic segmentation in the context of street scenes and train semantic segmentation networks on combinations of various datasets. In Chapter 2 we design a framework of hierarchical classifiers over a single convolutional backbone, and train it end-to-end on a combination of pixel-labeled datasets, improving generalizability and the number of recognizable semantic concepts. Chapter 3 focuses on enriching semantic segmentation with weak supervision and proposes a weakly-supervised algorithm for training with bounding box-level and image-level supervision instead of only with per-pixel supervision. The memory and computational load challenges that arise from simultaneous training on multiple datasets are addressed in Chapter 4. We propose two methodologies for selecting informative and diverse samples from datasets with weak supervision to reduce our networks' ecological footprint without sacrificing performance. Motivated by memory and computation efficiency requirements, in Chapter 5, we rethink simultaneous training on heterogeneous datasets and propose a universal semantic segmentation framework. This framework achieves consistent increases in performance metrics and semantic knowledgeability by exploiting various scene understanding datasets. Chapter 6 introduces the novel task of part-aware panoptic segmentation, which extends our reasoning towards holistic scene understanding. This task combines scene and parts-level semantics with instance-level object detection. In conclusion, our contributions span over convolutional network architectures, weakly-supervised learning, part and panoptic segmentation, paving the way towards a holistic, rich, and sustainable visual scene understanding.