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.

Deep learning techniques have been hugely successful for traditional supervised and unsupervised machine learning problems. In large part, these techniques solve continuous optimization problems. Recently however, discrete generative deep learning models have been successfully used to efficiently search high-dimensional discrete spaces. These methods work by representing discrete objects as sequences, for which powerful sequence-based deep models can be employed. Unfortunately, these techniques are significantly hindered by the fact that these generative models often produce invalid sequences. As a step towards solving this problem, we propose to learn a deep recurrent validator model. Given a partial sequence, our model learns the probability of that sequence occurring as the beginning of a full valid sequence. Thus this identifies valid versus invalid sequences and crucially it also provides insight about how individual sequence elements influence the validity of discrete objects. To learn this model we propose an approach inspired by seminal work in Bayesian active learning. On a synthetic dataset, we demonstrate the ability of our model to distinguish valid and invalid sequences. We believe this is a key step toward learning generative models that faithfully produce valid discrete objects.

Accurately predicting the time of occurrence of an event of interest is a critical problem in longitudinal data analysis. One of the main challenges in this context is the presence of instances whose event outcomes become unobservable after a certain time point or when some instances do not experience any event during the monitoring period. Such a phenomenon is called censoring which can be effectively handled using survival analysis techniques. Traditionally, statistical approaches have been widely developed in the literature to overcome this censoring issue. In addition, many machine learning algorithms are adapted to effectively handle survival data and tackle other challenging problems that arise in real-world data. In this survey, we provide a comprehensive and structured review of the representative statistical methods along with the machine learning techniques used in survival analysis and provide a detailed taxonomy of the existing methods. We also discuss several topics that are closely related to survival analysis and illustrate several successful applications in various real-world application domains. We hope that this paper will provide a more thorough understanding of the recent advances in survival analysis and offer some guidelines on applying these approaches to solve new problems that arise in applications with censored data.

Recommender systems (RS) help users navigate large sets of items in the search for "interesting" ones. One approach to RS is Collaborative Filtering (CF), which is based on the idea that similar users are interested in similar items. Most model-based approaches to CF seek to train a machine-learning/data-mining model based on sparse data; the model is then used to provide recommendations. While most of the proposed approaches are effective for small-size situations, the combinatorial nature of the problem makes it impractical for medium-to-large instances. In this work we present a novel approach to CF that works by training a Denoising Auto-Encoder (DAE) on corrupted baskets, i.e., baskets from which one or more items have been removed. The DAE is then forced to learn to reconstruct the original basket given its corrupted input. Due to recent advancements in optimization and other technologies for training neural-network models (such as DAE), the proposed method results in a scalable and practical approach to CF. The contribution of this work is twofold: (1) to identify missing items in observed baskets and, thus, directly providing a CF model; and, (2) to construct a generative model of baskets which may be used, for instance, in simulation analysis or as part of a more complex analytical method.

There exist two main approaches to automatically extract affective orientation: lexicon-based and corpus-based. In this work, we argue that these two methods are compatible and show that combining them can improve the accuracy of emotion classifiers. In particular, we introduce a novel variant of the Label Propagation algorithm that is tailored to distributed word representations, we apply batch gradient descent to accelerate the optimization of label propagation and to make the optimization feasible for large graphs, and we propose a reproducible method for emotion lexicon expansion. We conclude that label propagation can expand an emotion lexicon in a meaningful way and that the expanded emotion lexicon can be leveraged to improve the accuracy of an emotion classifier.

While Multiple Instance (MI) data are point patterns -- sets or multi-sets of unordered points -- appropriate statistical point pattern models have not been used in MI learning. This article proposes a framework for model-based MI learning using point process theory. Likelihood functions for point pattern data derived from point process theory enable principled yet conceptually transparent extensions of learning tasks, such as classification, novelty detection and clustering, to point pattern data. Furthermore, tractable point pattern models as well as solutions for learning and decision making from point pattern data are developed.

In practice, proper tuning of t-SNE perplexity requires users to understand the inner working of the method as well as to have hands-on experience. We propose a model selection objective for t-SNE perplexity that requires negligible extra computation beyond that of the t-SNE itself. We empirically validate that the perplexity settings found by our approach are consistent with preferences elicited from human experts across a number of datasets. The similarities of our approach to Bayesian information criteria (BIC) and minimum description length (MDL) are also analyzed.

In recent years, the search for numerical algorithms which return probability distributions over the solution for a given numerical problem has become an active area of research [25]. Several models and methods have been proposed for the solution of initial value problems (IVPs) [57, 7, 51, 9, 31, 61]. However, these probabilistic algorithms have no immediate connection to the extensive literature on this task in numerical analysis. Most importantly, such inference algorithms do not come with convergence analysis out of the box. The methods in [7, 9, 61] have convergence results, but their respective implementations are based on sampling schemes and, thus, do not offer guarantees for individual runs. The methods in [51, 31] offer a deterministic execution and an analytical guarantee for the first step, but we will show that this guarantee is lacking for the whole integration domain. In this paper, we present a class of probabilistic solvers which combine properties of the standard and the probabilistic algorithms. We formulate desiderata that users might have for a probabilistic numerical algorithm.

Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by extending some standard probabilistic modelling tools to the circular domain. First we introduce a new multivariate distribution over circular variables, called the multivariate Generalised von Mises (mGvM) distribution. This distribution can be constructed by restricting and renormalising a general multivariate Gaussian distribution to the unit hyper-torus. Previously proposed multivariate circular distributions are shown to be special cases of this construction. Second, we introduce a new probabilistic model for circular regression, that is inspired by Gaussian Processes, and a method for probabilistic principal component analysis with circular hidden variables. These models can leverage standard modelling tools (e.g. covariance functions and methods for automatic relevance determination). Third, we show that the posterior distribution in these models is a mGvM distribution which enables development of an efficient variational free-energy scheme for performing approximate inference and approximate maximum-likelihood learning.