Finally, a comprehensive hands-on machine learning course with specific focus on classification based models for the investment community and passionate investors. In the past few years, there has been a massive adoption and growth in the use of data science, artificial intelligence and machine learning to find alpha. However, information on and application of machine learning to investment are scarce. This course has been designed to address that. It is meant to spark your creative juices and get you started in this space.

In evolving complex systems such as air traffic and social organizations, collective effects emerge from their many components' dynamic interactions. While the dynamic interactions can be represented by temporal networks with nodes and links that change over time, they remain highly complex. It is therefore often necessary to use methods that extract the temporal networks' large-scale dynamic community structure. However, such methods are subject to overfitting or suffer from effects of arbitrary, a priori imposed timescales, which should instead be extracted from data. Here we simultaneously address both problems and develop a principled data-driven method that determines relevant timescales and identifies patterns of dynamics that take place on networks as well as shape the networks themselves. We base our method on an arbitrary-order Markov chain model with community structure, and develop a nonparametric Bayesian inference framework that identifies the simplest such model that can explain temporal interaction data.

As datasets capturing human choices grow in richness and scale--particularly in online domains--there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not assume any of the above axioms while still satisfying the foundational axiom of uniform expansion, a considerably weaker assumption than Luce's choice axiom. We show that the PCMC model significantly outperforms both the Multinomial Logit (MNL) model and a mixed MNL (MMNL) model in prediction tasks on both synthetic and empirical datasets known to exhibit violations of Luce's axiom. Our analysis also synthesizes several recent observations connecting the Multinomial Logit model and Markov chains; the PCMC model retains the Multinomial Logit model as a special case.

Like the course I just released on Hidden Markov Models, Recurrent Neural Networks are all about learning sequences - but whereas Markov Models are limited by the Markov assumption, Recurrent Neural Networks are not - and as a result, they are more expressive, and more powerful than anything we've seen on tasks that we haven't made progress on in decades. So what's going to be in this course and how will it build on the previous neural network courses and Hidden Markov Models? In the first section of the course we are going to add the concept of time to our neural networks. I'll introduce you to the Simple Recurrent Unit, also known as the Elman unit. We are going to revisit the XOR problem, but we're going to extend it so that it becomes the parity problem - you'll see that regular feedforward neural networks will have trouble solving this problem but recurrent networks will work because the key is to treat the input as a sequence.

The partially observable Markov decision process (POMDP) provides a principled general framework for planning under uncertainty, but solving POMDPs optimally is computationally intractable, due to the "curse of dimensionality" and the "curse of history". To overcome these challenges, we introduce the Determinized Sparse Partially Observable Tree (DESPOT), a sparse approximation of the standard belief tree, for online planning under uncertainty. A DESPOT focuses online planning on a set of randomly sampled scenarios and compactly captures the "execution" of all policies under these scenarios. We show that the best policy obtained from a DESPOT is near-optimal, with a regret bound that depends on the representation size of the optimal policy. Leveraging this result, we give an anytime online planning algorithm, which searches a DESPOT for a policy that optimizes a regularized objective function. Regularization balances the estimated value of a policy under the sampled scenarios and the policy size, thus avoiding overfitting. The algorithm demonstrates strong experimental results, compared with some of the best online POMDP algorithms available. It has also been incorporated into an autonomous driving system for real-time vehicle control. The source code for the algorithm is available online.

We consider the problem of active feature acquisition, where we sequentially select the subset of features in order to achieve the maximum prediction performance in the most cost-effective way. In this work, we formulate this active feature acquisition problem as a reinforcement learning problem, and provide a novel framework for jointly learning both the RL agent and the classifier (environment). We also introduce a more systematic way of encoding subsets of features that can properly handle innate challenge with missing entries in active feature acquisition problems, that uses the orderless LSTM-based set encoding mechanism that readily fits in the joint learning framework. We evaluate our model on a carefully designed synthetic dataset for the active feature acquisition as well as several real datasets such as electric health record (EHR) datasets, on which it outperforms all baselines in terms of prediction performance as well feature acquisition cost.

We present a probabilistic framework for nonlinearities, based on doubly truncated Gaussian distributions. By setting the truncation points appropriately, we are able to generate various types of nonlinearities within a unified framework, including sigmoid, tanh and ReLU, the most commonly used nonlinearities in neural networks. The framework readily integrates into existing stochastic neural networks (with hidden units characterized as random variables), allowing one for the first time to learn the nonlinearities alongside model weights in these networks. Extensive experiments demonstrate the performance improvements brought about by the proposed framework when integrated with the restricted Boltzmann machine (RBM), temporal RBM and the truncated Gaussian graphical model (TGGM).

Approximate Markov chain Monte Carlo (MCMC) offers the promise of more rapid sampling at the cost of more biased inference. Since standard MCMC diagnostics fail to detect these biases, researchers have developed computable Stein discrepancy measures that provably determine the convergence of a sample to its target distribution. This approach was recently combined with the theory of reproducing kernels to define a closed-form kernel Stein discrepancy (KSD) computable by summing kernel evaluations across pairs of sample points. We develop a theory of weak convergence for KSDs based on Stein's method, demonstrate that commonly used KSDs fail to detect non-convergence even for Gaussian targets, and show that kernels with slowly decaying tails provably determine convergence for a large class of target distributions. The resulting convergence-determining KSDs are suitable for comparing biased, exact, and deterministic sample sequences and simpler to compute and parallelize than alternative Stein discrepancies. We use our tools to compare biased samplers, select sampler hyperparameters, and improve upon existing KSD approaches to one-sample hypothesis testing and sample quality improvement.

We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to switch from one function to another. Thus each curve follows what we call a switching nonparametric regression model. We develop an EM algorithm to estimate the model parameters. We also obtain standard errors for the parameter estimates of the state process. We consider several types of state processes: independent and identically distributed, independent but depending on a covariate and Markov. Simulation studies show the frequentist properties of our estimates. We apply our methods to a data set of a building's power usage.

Department of Informatics, King's College London; osvaldo.simeone@kcl.ac.uk ABSTRACT This monograph aims at providing an introduction to key concepts, algorithms, and theoretical frameworks in machine learning, including supervised and unsupervised learning, statistical learning theory, probabilistic graphical models and approximate inference. The intended readership consists of electrical engineers with a background in probability and linear algebra. The treatment builds on first principles, and organizes the main ideas according to clearly defined categories, such as discriminative and generative models, frequentist and Bayesian approaches, exact and approximate inference, directed and undirected models, and convex and non-convex optimization. The mathematical framework uses information-theoretic measures as a unifying tool. The text offers simple and reproducible numerical examples providing insights into key motivations and conclusions. Rather than providing exhaustive details on the existing myriad solutions in each specific category, for which the reader is referred to textbooks and papers, this monograph is meant as an entry point for an engineer into the literature on machine learning.