The Hidden Markov Model or HMM is all about learning sequences. A lot of the data that would be very useful for us to model is in sequences. Stock prices are sequences of prices. Language is a sequence of words. Credit scoring involves sequences of borrowing and repaying money, and we can use those sequences to predict whether or not you're going to default.

The analysis of mixed data has been raising challenges in statistics and machine learning. One of two most prominent challenges is to develop new statistical techniques and methodologies to effectively handle mixed data by making the data less heterogeneous with minimum loss of information. The other challenge is that such methods must be able to apply in large-scale tasks when dealing with huge amount of mixed data. To tackle these challenges, we introduce parameter sharing and balancing extensions to our recent model, the mixed-variate restricted Boltzmann machine (MV.RBM) which can transform heterogeneous data into homogeneous representation. We also integrate structured sparsity and distance metric learning into RBM-based models. Our proposed methods are applied in various applications including latent patient profile modelling in medical data analysis and representation learning for image retrieval. The experimental results demonstrate the models perform better than baseline methods in medical data and outperform state-of-the-art rivals in image dataset.

Under Markovian assumptions, we leverage a Central Limit Theorem (CLT) for the empirical measure in the test statistic of the composite hypothesis Hoeffding test so as to establish weak convergence results for the test statistic, and, thereby, derive a new estimator for the threshold needed by the test. We first show the advantages of our estimator over an existing estimator by conducting extensive numerical experiments. We find that our estimator controls better for false alarms while maintaining satisfactory detection probabilities. We then apply the Hoeffding test with our threshold estimator to detecting anomalies in two distinct applications domains: one in communication networks and the other in transportation networks. The former application seeks to enhance cyber security and the latter aims at building smarter transportation systems in cities.

About this course: In previous courses in the Specialization, we have discussed how to sequence and compare genomes. This course will cover advanced topics in finding mutations lurking within DNA and proteins. In the first half of the course, we would like to ask how an individual's genome differs from the "reference genome" of the species. Our goal is to take small fragments of DNA from the individual and "map" them to the reference genome. We will see that the combinatorial pattern matching algorithms solving this problem are elegant and extremely efficient, requiring a surprisingly small amount of runtime and memory.

Sampling from the posterior distribution using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations to fully explore the correct posterior. This is often the case when the posterior of interest is multi-modal, as the MCMC sampler can become trapped in a local mode for a large number of iterations. In this paper, we introduce the pseudo-extended MCMC method as an approach for improving the mixing of the MCMC sampler in complex posterior distributions. The pseudo-extended method augments the state-space of the posterior using pseudo-samples as auxiliary variables, where on the extended space, the MCMC sampler is able to easily move between the well-separated modes of the posterior. We apply the pseudo-extended method within an Hamiltonian Monte Carlo sampler and show that by using the No U-turn algorithm (Hoffman and Gelman, 2014), our proposed sampler is completely tuning free. We compare the pseudo-extended method against well-known tempered MCMC algorithms and show the advantages of the new sampler on a number of challenging examples from the statistics literature.

Natural-language-facilitated human-robot cooperation (NLC) refers to using natural language (NL) to facilitate interactive information sharing and task executions with a common goal constraint between robots and humans. Recently, NLC research has received increasing attention. Typical NLC scenarios include robotic daily assistance, robotic health caregiving, intelligent manufacturing, autonomous navigation, and robot social accompany. However, a thorough review, that can reveal latest methodologies to use NL to facilitate human-robot cooperation, is missing. In this review, a comprehensive summary about methodologies for NLC is presented. NLC research includes three main research focuses: NL instruction understanding, NL-based execution plan generation, and knowledge-world mapping. In-depth analyses on theoretical methods, applications, and model advantages and disadvantages are made. Based on our paper review and perspective, potential research directions of NLC are summarized.

Since computers can automate such processes, automatic music generation has become a small, but steadily emerging field in Artificial Intelligence and Machine Learning. Nevertheless, automatic music generation as a problem is far from solved: musical outputs created by artificial systems are regarded as a curiosity by human listeners at best, but all too often they are taken as a direct offense to our sense of musical aesthetics. This sensitivity to violations of even the most subtle musical norms illustrates how complex the problem of (especially polyphonic) music generation is. In addition, there are hardly any objective evaluation criteria to rigorously test and compare music generation systems. This is lamentable, not least since successful methods for automatic music generation would be of considerable commercial interest to the music, gaming, and film industries.

Microsoft is working on an autonomous aircraft that can fly for long periods of time without any power. Rather than a motor, the glider relies on artificial intelligence that mimics how birds fly, autonomously finding thermals, or invisible columns of air that rise due to heat, to carry it for long distances. A recent test of the 16.5-foot aircraft - called a sailplane - conducted in the middle of the desert in Hawthorne, Nevada proved successful - the algorithms researchers developed to help it predict where thermals would appear next worked and kept it aloft. Microsoft is working on an autonomous aircraft that can fly for long periods of time without any power. 'Birds do this seamlessly, and all they're doing is harnessing nature,' Ashish Kapoor, a principal researcher at Microsoft, said.

This survey explores Procedural Content Generation via Machine Learning (PCGML), defined as the generation of game content using machine learning models trained on existing content. As the importance of PCG for game development increases, researchers explore new avenues for generating high-quality content with or without human involvement; this paper addresses the relatively new paradigm of using machine learning (in contrast with search-based, solver-based, and constructive methods). We focus on what is most often considered functional game content such as platformer levels, game maps, interactive fiction stories, and cards in collectible card games, as opposed to cosmetic content such as sprites and sound effects. In addition to using PCG for autonomous generation, co-creativity, mixed-initiative design, and compression, PCGML is suited for repair, critique, and content analysis because of its focus on modeling existing content. We discuss various data sources and representations that affect the resulting generated content. Multiple PCGML methods are covered, including neural networks, long short-term memory (LSTM) networks, autoencoders, and deep convolutional networks; Markov models, $n$-grams, and multi-dimensional Markov chains; clustering; and matrix factorization. Finally, we discuss open problems in the application of PCGML, including learning from small datasets, lack of training data, multi-layered learning, style-transfer, parameter tuning, and PCG as a game mechanic.

It is well established that neural networks with deep architectures perform better than shallow networks for many tasks in machine learning. In statistical physics, while there has been recent interest in representing physical data with generative modelling, the focus has been on shallow neural networks. A natural question to ask is whether deep neural networks hold any advantage over shallow networks in representing such data. We investigate this question by using unsupervised, generative graphical models to learn the probability distribution of a two-dimensional Ising system. Deep Boltzmann machines, deep belief networks, and deep restricted Boltzmann networks are trained on thermal spin configurations from this system, and compared to the shallow architecture of the restricted Boltzmann machine. We benchmark the models, focussing on the accuracy of generating energetic observables near the phase transition, where these quantities are most difficult to approximate. Interestingly, after training the generative networks, we observe that the accuracy essentially depends only on the number of neurons in the first hidden layer of the network, and not on other model details such as network depth or model type. This is evidence that shallow networks are more efficient than deep networks at representing physical probability distributions associated with Ising systems near criticality.