In many statistical learning problems, the target functions to be optimized are highly non-convex in various model spaces and thus are difficult to analyze. In this paper, we compute \emph{Energy Landscape Maps} (ELMs) which characterize and visualize an energy function with a tree structure, in which each leaf node represents a local minimum and each non-leaf node represents the barrier between adjacent energy basins. The ELM also associates each node with the estimated probability mass and volume for the corresponding energy basin. We construct ELMs by adopting the generalized Wang-Landau algorithm and multi-domain sampler that simulates a Markov chain traversing the model space by dynamically reweighting the energy function. We construct ELMs in the model space for two classic statistical learning problems: i) clustering with Gaussian mixture models or Bernoulli templates; and ii) bi-clustering. We propose a way to measure the difficulties (or complexity) of these learning problems and study how various conditions affect the landscape complexity, such as separability of the clusters, the number of examples, and the level of supervision; and we also visualize the behaviors of different algorithms, such as K-mean, EM, two-step EM and Swendsen-Wang cuts, in the energy landscapes.

Restricted Boltzmann Machines (RBMs) are one of the fundamental building blocks of deep learning. Approximate maximum likelihood training of RBMs typically necessitates sampling from these models. In many training scenarios, computationally efficient Gibbs sampling procedures are crippled by poor mixing. In this work we propose a novel method of sampling from Boltzmann machines that demonstrates a computationally efficient way to promote mixing. Our approach leverages an under-appreciated property of deep generative models such as the Deep Belief Network (DBN), where Gibbs sampling from deeper levels of the latent variable hierarchy results in dramatically increased ergodicity. Our approach is thus to train an auxiliary latent hierarchical model, based on the DBN. When used in conjunction with parallel-tempering, the method is asymptotically guaranteed to simulate samples from the target RBM. Experimental results confirm the effectiveness of this sampling strategy in the context of RBM training.

In this paper we describe a hierarchical method for procedurallygenerating maps using Markov chains. Ourmethod takes as input a collection of human-authoredtwo-dimensional maps, and splits them into high-leveltiles which capture large structures. Markov chains arethen learned from those maps to capture the structure ofboth the high-level tiles, as well as the low-level tiles.Then, the learned Markov chains are used to generatenew maps by first generating the high-level structure ofthe map using high-level tiles, and then generating thelow-level layout of the map. We validate our approachusing the game Super Mario Bros., by evaluating thequality of maps produced using different configurationsfor training and generation.

While many open-ended digital games feature non-linear storylines and multiple solution paths, it is challenging for game developers to create effective game experiences in these settings due to the freedom given to the player. To address these challenges, goal recognition, a computational player-modeling task, has been investigated to enable digital games to dynamically predict players’ goals. This paper presents a goal recognition framework based on stacked denoising autoencoders, a variant of deep learning. The learned goal recognition models, which are trained from a corpus of player interactions, not only offer improved performance, but also offer the substantial advantage of eliminating the need for labor-intensive feature engineering. An evaluation demonstrates that the deep learning-based goal recognition framework significantly outperforms the previous state-of-the-art goal recognition approach based on Markov logic networks.

In this tutorial we explain the inference procedures developed for the sparse Gaussian process (GP) regression and Gaussian process latent variable model (GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias & Lawrence (2010) is brief, hence getting a full picture of it requires collecting results from several different sources and a substantial amount of algebra to fill-in the gaps. Our main goal is thus to collect all the results and full derivations into one place to help speed up understanding this work. In doing so we present a re-parametrisation of the inference that allows it to be carried out in parallel. A secondary goal for this document is, therefore, to accompany our paper and open-source implementation of the parallel inference scheme for the models. We hope that this document will bridge the gap between the equations as implemented in code and those published in the original papers, in order to make it easier to extend existing work. We assume prior knowledge of Gaussian processes and variational inference, but we also include references for further reading where appropriate.

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates, robustness to over-fitting, and principled ways for tuning hyper-parameters. However the scalability of these models to big datasets remains an active topic of research. We introduce a novel re-parametrisation of variational inference for sparse GP regression and latent variable models that allows for an efficient distributed algorithm. This is done by exploiting the decoupling of the data given the inducing points to re-formulate the evidence lower bound in a Map-Reduce setting. We show that the inference scales well with data and computational resources, while preserving a balanced distribution of the load among the nodes. We further demonstrate the utility in scaling Gaussian processes to big data. We show that GP performance improves with increasing amounts of data in regression (on flight data with 2 million records) and latent variable modelling (on MNIST). The results show that GPs perform better than many common models often used for big data.

Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large scale models. This paper presents full Bayesian inference via VB on both single and coupled tensor factorization models. Our method can be run even for very large models and is easily implemented. It exhibits better prediction performance than existing approaches based on maximum likelihood on several real-world datasets for missing link prediction problem.

Concept map is a graphical tool for representing knowledge. They have been used in many different areas, including education, knowledge management, business and intelligence. Constructing of concept maps manually can be a complex task; an unskilled person may encounter difficulties in determining and positioning concepts relevant to the problem area. An application that recommends concept candidates and their position in a concept map can significantly help the user in that situation. This paper gives an overview of different approaches to automatic and semi-automatic creation of concept maps from textual and non-textual sources. The concept map mining process is defined, and one method suitable for the creation of concept maps from unstructured textual sources in highly inflected languages such as the Croatian language is described in detail. Proposed method uses statistical and data mining techniques enriched with linguistic tools. With minor adjustments, that method can also be used for concept map mining from textual sources in other morphologically rich languages.

In (exploratory) factor analysis, the loading matrix is identified only up to orthogonal rotation. For identifiability, one thus often takes the loading matrix to be lower triangular with positive diagonal entries. In Bayesian inference, a standard practice is then to specify a prior under which the loadings are independent, the off-diagonal loadings are normally distributed, and the diagonal loadings follow a truncated normal distribution. This prior specification, however, depends in an important way on how the variables and associated rows of the loading matrix are ordered. We show how a minor modification of the approach allows one to compute with the identifiable lower triangular loading matrix but maintain invariance properties under reordering of the variables.

We consider online planning in Markov decision processes (MDPs). In online planning, the agent focuses on its current state only, deliberates about the set of possible policies from that state onwards and, when interrupted, uses the outcome of that exploratory deliberation to choose what action to perform next. Formally, the performance of algorithms for online planning is assessed in terms of simple regret, the agent's expected performance loss when the chosen action, rather than an optimal one, is followed. To date, state-of-the-art algorithms for online planning in general MDPs are either best effort, or guarantee only polynomial-rate reduction of simple regret over time. Here we introduce a new Monte-Carlo tree search algorithm, BRUE, that guarantees exponential-rate and smooth reduction of simple regret. At a high level, BRUE is based on a simple yet non-standard state-space sampling scheme, MCTS2e, in which different parts of each sample are dedicated to different exploratory objectives. We further extend BRUE with a variant of ``learning by forgetting.'' The resulting parametrized algorithm, BRUE(alpha), exhibits even more attractive formal guarantees than BRUE. Our empirical evaluation shows that both BRUE and its generalization, BRUE(alpha), are also very effective in practice and compare favorably to the state-of-the-art.