Statistical Learning
Best Machine Learning books, courses & tutorials 2018 - ReactDOM
Machine Learning A-Z: Hands-On Python & R In Data Science by Kirill Eremenko, Hadelin de Ponteves and SuperDataScience Team will teach you Machine Learning using Python & R. These Python videos will teach you everything related to Machine Learning. You will build an army of powerful Machine Learning models. Then you will combine them to solve any problem. You will be able to handle different topics like Reinforcement Learning, NLP and Deep Learning. Using the knowledge you gain, you will know which Machine Learning model to use depending on the problem.
Hierarchical (Deep) Echo State Networks with Uncertainty Quantification for Spatio-Temporal Forecasting
McDermott, Patrick L., Wikle, Christopher K.
Long-lead forecasting for spatio-temporal problems can often entail complex nonlinear dynamics that are difficult to specify it a priori. Current statistical methodologies for modeling these processes are often overparameterized and thus, struggle from a computational perspective. One potential parsimonious solution to this problem is a method from the dynamical systems and engineering literature referred to as an echo state network (ESN). ESN models use so-called reservoir computing to efficiently estimate a dynamical neural network forecast, model referred to as a recurrent neural network (RNN). Moreover, so-called deep models have recently been shown to be successful at predicting high-dimensional complex nonlinear processes. These same traits can be used to characterize many spatio-temporal processes. Here we introduce a deep ensemble ESN (D-EESN) model. Through the use of an ensemble framework, this model is able to generate forecasts that are accompanied by uncertainty estimates. After introducing the D-EESN, we then develop a hierarchical Bayesian implementation. We use a general hierarchical Bayesian framework that accommodates non-Gaussian data types and multiple levels of uncertainties. The proposed methodology is first applied to a data set simulated from a novel non-Gaussian multiscale Lorenz-96 dynamical system simulation model and then to a long-lead United States (U.S.) soil moisture forecasting application.
Contextual bandits with surrogate losses: Margin bounds and efficient algorithms
Foster, Dylan J., Krishnamurthy, Akshay
We introduce a new family of margin-based regret guarantees for adversarial contextual bandit learning. Our results are based on multiclass surrogate losses. Using the ramp loss, we derive a universal margin-based regret bound in terms of the sequential metric entropy for a benchmark class of real-valued regression functions. The new margin bound serves as a complete contextual bandit analogue of the classical margin bound from statistical learning. The result applies to large nonparametric classes, improving on the best known results for Lipschitz contextual bandits (Cesa-Bianchi et al., 2017) and, as a special case, generalizes the dimension-independent Banditron regret bound (Kakade et al., 2008) to arbitrary linear classes with smooth norms. On the algorithmic side, we use the hinge loss to derive an efficient algorithm with a $\sqrt{dT}$-type mistake bound against benchmark policies induced by $d$-dimensional regression functions. This provides the first hinge loss-based solution to the open problem of Abernethy and Rakhlin (2009). With an additional i.i.d. assumption we give a simple oracle-efficient algorithm whose regret matches our generic metric entropy-based bound for sufficiently complex nonparametric classes. Under realizability assumptions our results also yield classical regret bounds.
Data Efficient Lithography Modeling with Transfer Learning and Active Data Selection
Lin, Yibo, Li, Meng, Watanabe, Yuki, Kimura, Taiki, Matsunawa, Tetsuaki, Nojima, Shigeki, Pan, David Z.
Lithography simulation is one of the key steps in physical verification, enabled by the substantial optical and resist models. A resist model bridges the aerial image simulation to printed patterns. While the effectiveness of learning-based solutions for resist modeling has been demonstrated, they are considerably data-demanding. Meanwhile, a set of manufactured data for a specific lithography configuration is only valid for the training of one single model, indicating low data efficiency. Due to the complexity of the manufacturing process, obtaining enough data for acceptable accuracy becomes very expensive in terms of both time and cost, especially during the evolution of technology generations when the design space is intensively explored. In this work, we propose a new resist modeling framework for contact layers, utilizing existing data from old technology nodes and active selection of data in a target technology node, to reduce the amount of data required from the target lithography configuration. Our framework based on transfer learning and active learning techniques is effective within a competitive range of accuracy, i.e., 3-10X reduction on the amount of training data with comparable accuracy to the state-of-the-art learning approach.
Uncoupled isotonic regression via minimum Wasserstein deconvolution
Rigollet, Philippe, Weed, Jonathan
Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function $f$ from independent pairs $(x_i, y_i)$ where $\mathbb{E}[y_i]=f(x_i), i=1, \ldots n$. While this problem is well understood both statistically and computationally, much less is known about its uncoupled counterpart where one is given only the unordered sets $\{x_1, \ldots, x_n\}$ and $\{y_1, \ldots, y_n\}$. In this work, we leverage tools from optimal transport theory to derive minimax rates under weak moments conditions on $y_i$ and to give an efficient algorithm achieving optimal rates. Both upper and lower bounds employ moment-matching arguments that are also pertinent to learning mixtures of distributions and deconvolution.
Empirical Risk Minimization and Stochastic Gradient Descent for Relational Data
Veitch, Victor, Austern, Morgane, Zhou, Wenda, Blei, David M., Orbanz, Peter
Empirical risk minimization is the principal tool for prediction problems, but its extension to relational data remains unsolved. We solve this problem using recent advances in graph sampling theory. We (i) define an empirical risk for relational data and (ii) obtain stochastic gradients for this risk that are automatically unbiased. The key ingredient is to consider the method by which data is sampled from a graph as an explicit component of model design. Theoretical results establish that the choice of sampling scheme is critical. By integrating fast implementations of graph sampling schemes with standard automatic differentiation tools, we are able to solve the risk minimization in a plug-and-play fashion even on large datasets. We demonstrate empirically that relational ERM models achieve state-of-the-art results on semi-supervised node classification tasks. The experiments also confirm the importance of the choice of sampling scheme.
Bayesian Model-Agnostic Meta-Learning
Kim, Taesup, Yoon, Jaesik, Dia, Ousmane, Kim, Sungwoong, Bengio, Yoshua, Ahn, Sungjin
Learning to infer Bayesian posterior from a few-shot dataset is an important step towards robust meta-learning due to the model uncertainty inherent in the problem. In this paper, we propose a novel Bayesian model-agnostic meta-learning method. The proposed method combines scalable gradient-based meta-learning with nonparametric variational inference in a principled probabilistic framework. During fast adaptation, the method is capable of learning complex uncertainty structure beyond a point estimate or a simple Gaussian approximation. In addition, a robust Bayesian meta-update mechanism with a new meta-loss prevents overfitting during meta-update. Remaining an efficient gradient-based meta-learner, the method is also model-agnostic and simple to implement. Experiment results show the accuracy and robustness of the proposed method in various tasks: sinusoidal regression, image classification, active learning, and reinforcement learning.
TopoReg: A Topological Regularizer for Classifiers
Chen, Chao, Ni, Xiuyan, Bai, Qinxun, Wang, Yusu
Regularization plays a crucial role in supervised learning. A successfully regularized model strikes a balance between a perfect description of the training data and the ability to generalize to unseen data. Most existing methods enforce a global regularization in a structure agnostic manner. In this paper, we initiate a new direction and propose to enforce the structural simplicity of the classification boundary by regularizing over its topological complexity. In particular, our measurement of topological complexity incorporates the importance of topological features (e.g., connected components, handles, and so on) in a meaningful manner, and provides a direct control over spurious topological structures. We incorporate the new measurement as a topological loss in training classifiers. We also propose an efficient algorithm to compute the gradient. Our method provides a novel way to topologically simplify the global structure of the model, without having to sacrifice too much of the flexibility of the model. We demonstrate the effectiveness of our new topological regularizer on a range of synthetic and real-world datasets.
Adversarial Distillation of Bayesian Neural Network Posteriors
Wang, Kuan-Chieh, Vicol, Paul, Lucas, James, Gu, Li, Grosse, Roger, Zemel, Richard
Bayesian neural networks (BNNs) allow us to reason about uncertainty in a principled way. Stochastic Gradient Langevin Dynamics (SGLD) enables efficient BNN learning by drawing samples from the BNN posterior using mini-batches. However, SGLD and its extensions require storage of many copies of the model parameters, a potentially prohibitive cost, especially for large neural networks. We propose a framework, Adversarial Posterior Distillation, to distill the SGLD samples using a Generative Adversarial Network (GAN). At test-time, samples are generated by the GAN. We show that this distillation framework incurs no loss in performance on recent BNN applications including anomaly detection, active learning, and defense against adversarial attacks. By construction, our framework not only distills the Bayesian predictive distribution, but the posterior itself. This allows one to compute quantities such as the approximate model variance, which is useful in downstream tasks. To our knowledge, these are the first results applying MCMC-based BNNs to the aforementioned downstream applications.
The decoupled extended Kalman filter for dynamic exponential-family factorization models
Gomez-Uribe, Carlos Alberto, Karrer, Brian
We specialize the decoupled extended Kalman filter (DEKF) for online parameter learning in factorization models, including factorization machines, matrix and tensor factorization, and illustrate the effectiveness of the approach through simulations. Learning model parameters through the DEKF makes factorization models more broadly useful by allowing for more flexible observations through the entire exponential family, modeling parameter drift, and producing parameter uncertainty estimates that can enable explore/exploit and other applications. We use a more general dynamics of the parameters than the standard DEKF, allowing parameter drift while encouraging reasonable values. We also present an alternate derivation of the regular extended Kalman filter and DEKF that connects these methods to natural gradient methods, and suggests a similarly decoupled version of the iterated extended Kalman filter.