We introduce the active exploration problem in Markov decision processes (MDPs). Each state of the MDP is characterized by a random value and the learner should gather samples to estimate the mean value of each state as accurately as possible. Similarly to active exploration in multi-armed bandit (MAB), states may have different levels of noise, so that the higher the noise, the more samples are needed. As the noise level is initially unknown, we need to trade off the exploration of the environment to estimate the noise and the exploitation of these estimates to compute a policy maximizing the accuracy of the mean predictions. We introduce a novel learning algorithm to solve this problem showing that active exploration in MDPs may be significantly more difficult than in MAB. We also derive a heuristic procedure to mitigate the negative effect of slowly mixing policies. Finally, we validate our findings on simple numerical simulations.

How do organisms recognize their environment by acquiring knowledge about the world, and what actions do they take based on this knowledge? This article examines hypotheses about organisms' adaptation to the environment from machine learning, information-theoretic, and thermodynamic perspectives. We start with constructing a hierarchical model of the world as an internal model in the brain, and review standard machine learning methods to infer causes by approximately learning the model under the maximum likelihood principle. This in turn provides an overview of the free energy principle for an organism, a hypothesis to explain perception and action from the principle of least surprise. Treating this statistical learning as communication between the world and brain, learning is interpreted as a process to maximize information about the world. We investigate how the classical theories of perception such as the infomax principle relates to learning the hierarchical model. We then present an approach to the recognition and learning based on thermodynamics, showing that adaptation by causal learning results in the second law of thermodynamics whereas inference dynamics that fuses observation with prior knowledge forms a thermodynamic process. These provide a unified view on the adaptation of organisms to the environment.

There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the type of the graph, the clustering approach, the inference approach, and whether the number of groups is selected or estimated. We then review unsupervised learning of texts, also known as topic modelling, as the two areas are closely related. Also reviewed are the models that combine block modelling with topic modelling, as such incorporations are natural because both areas have the same goal of model-based clustering. How different approaches cope with various issues will be summarised and compared, to facilitate the demand of practitioners for a concise overview of the current status of these two areas of literature.

Deep structured-prediction energy-based models combine the expressive power of learned representations and the ability of embedding knowledge about the task at hand into the system. A common way to learn parameters of such models consists in a multistage procedure where different combinations of components are trained at different stages. The joint end-to-end training of the whole system is then done as the last fine-tuning stage. This multistage approach is time-consuming and cumbersome as it requires multiple runs until convergence and multiple rounds of hyperparameter tuning. From this point of view, it is beneficial to start the joint training procedure from the beginning. However, such approaches often unexpectedly fail and deliver results worse than the multistage ones. In this paper, we hypothesize that one reason for joint training of deep energy-based models to fail is the incorrect relative normalization of different components in the energy function. We propose online and offline scaling algorithms that fix the joint training and demonstrate their efficacy on three different tasks.

The identification of anomalies in temporal data is a core component of numerous research areas such as intrusion detection, fault prevention, genomics and fraud detection. This article provides an experimental comparison of the novelty detection problem applied to discrete sequences. The objective of this study is to identify which state-of-the-art methods are efficient and appropriate candidates for a given use case. These recommendations rely on extensive novelty detection experiments based on a variety of public datasets in addition to novel industrial datasets. We also perform thorough scalability and memory usage tests resulting in new supplementary insights of the methods' performance, key selection criterion to solve problems relying on large volumes of data and to meet the expectations of applications subject to strict response time constraints.

Intuitively, the idea of a Naive Bayes is how you probably approach life. Like all my articles, I believe that a simple and intuitive understanding of a model should be understood first before diving into the mathematics and practical jargon. Let's say you're responsible for Thanksgiving dinner. You have cooked Thanksgiving dinner for the last ten years. Within those ten years, you have prepared three desserts: pumpkin pie, chocolate cheesecake, and white macadamia cookies.

Active learning methods for neural networks are usually based on greedy criteria which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one active learning iteration, or retraining the neural network after adding each data point, which is computationally inefficient. Moreover, uncertainty estimates for neural networks sometimes are overconfident for the points lying far from the training sample. In this work we propose to approximate Bayesian neural networks (BNN) by Gaussian processes, which allows us to update the uncertainty estimates of predictions efficiently without retraining the neural network, while avoiding overconfident uncertainty prediction for out-of-sample points. In a series of experiments on real-world data including large-scale problems of chemical and physical modeling, we show superiority of the proposed approach over the state-of-the-art methods.

It is well known that a small number of variables is often sufficient to effectively describe high-dimensional data. This number is called the intrinsic dimension (ID) of the data. What is not so commonly known is that the ID can vary within the same dataset. This fact has been highlighted in technical discussions, but seldom exploited to gain practical insight in the data structure. Here we develop a simple and robust approach to cluster regions with the same local ID in a given data landscape. Surprisingly, we find that many real-world data sets contain regions with widely heterogeneous dimensions. These regions host points differing in core properties: folded vs unfolded configurations in a protein molecular dynamics trajectory, active vs non-active regions in brain imaging data, and firms with different financial risk in company balance sheets. Our results show that a simple topological feature, the local ID, is sufficient to uncover a rich structure in high-dimensional data landscapes. Introduction From string theory to science fiction, the idea that we might be glued onto a lowdimensional surface embedded in a space of large dimensionality has tickled the speculations of scientists and writers alike. When it comes to multidimensional data, however, such situation is quite common rather than a wild speculation: data often concentrate on hypersurfaces of low intrinsic dimension (ID).

Methods for learning and planning in sequential decision problems often assume the learner is aware of all possible states and actions in advance. This assumption is sometimes untenable. In this paper, we give a method to learn factored markov decision problems from both domain exploration and expert assistance, which guarantees convergence to near-optimal behaviour, even when the agent begins unaware of factors critical to success. Our experiments show our agent learns optimal behaviour on small and large problems, and that conserving information on discovering new possibilities results in faster convergence.

The article is devoted to investigating the application of hedging strategies to online expert weight allocation under delayed feedback. As the main result, we develop the General Hedging algorithm $\mathcal{G}$ based on the exponential reweighing of experts' losses. We build the artificial probabilistic framework and use it to prove the adversarial loss bounds for the algorithm $\mathcal{G}$ in the delayed feedback setting. The designed algorithm $\mathcal{G}$ can be applied to both countable and continuous sets of experts. We also show how algorithm $\mathcal{G}$ extends classical Hedge (Multiplicative Weights) and adaptive Fixed Share algorithms to the delayed feedback and derive their regret bounds for the delayed setting by using our main result.