Spatial Monte Carlo integration (SMCI) is an extension of standard Monte Carlo integration and can approximate expectations on Markov random fields with high accuracy. SMCI was applied to pairwise Boltzmann machine (PBM) learning, with superior results to those from some existing methods. The approximation level of SMCI can be changed, and it was proved that a higher-order approximation of SMCI is statistically more accurate than a lower-order approximation. However, SMCI as proposed in the previous studies suffers from a limitation that prevents the application of a higher-order method to dense systems. This study makes two different contributions as follows. A generalization of SMCI (called generalized SMCI (GSMCI)) is proposed, which allows relaxation of the above-mentioned limitation; moreover, a statistical accuracy bound of GSMCI is proved. This is the first contribution of this study. A new PBM learning method based on SMCI is proposed, which is obtained by combining SMCI and the persistent contrastive divergence. The proposed learning method greatly improves the accuracy of learning. This is the second contribution of this study.

Reasoning with declarative knowledge (RDK) and sequential decision-making (SDM) are two key research areas in artificial intelligence. RDK methods reason with declarative domain knowledge, including commonsense knowledge, that is either provided a priori or acquired over time, while SDM methods (probabilistic planning and reinforcement learning) seek to compute action policies that maximize the expected cumulative utility over a time horizon; both classes of methods reason in the presence of uncertainty. Despite the rich literature in these two areas, researchers have not fully explored their complementary strengths. In this paper, we survey algorithms that leverage RDK methods while making sequential decisions under uncertainty. We discuss significant developments, open problems, and directions for future work.

Estimating time-varying graphical models are of paramount importance in various social, financial, biological, and engineering systems, since the evolution of such networks can be utilized for example to spot trends, detect anomalies, predict vulnerability, and evaluate the impact of interventions. Existing methods require extensive tuning of parameters that control the graph sparsity and temporal smoothness. Furthermore, these methods are computationally burdensome with time complexity O(NP^3) for P variables and N time points. As a remedy, we propose a low-complexity tuning-free Bayesian approach, named BADGE. Specifically, we impose temporally-dependent spike-and-slab priors on the graphs such that they are sparse and varying smoothly across time. A variational inference algorithm is then derived to learn the graph structures from the data automatically. Owning to the pseudo-likelihood and the mean-field approximation, the time complexity of BADGE is only O(NP^2). Additionally, by identifying the frequency-domain resemblance to the time-varying graphical models, we show that BADGE can be extended to learning frequency-varying inverse spectral density matrices, and yields graphical models for multivariate stationary time series. Numerical results on both synthetic and real data show that that BADGE can better recover the underlying true graphs, while being more efficient than the existing methods, especially for high-dimensional cases.

Strategic recommendations (SR) refer to the problem where an intelligent agent observes the sequential behaviors and activities of users and decides when and how to interact with them to optimize some long-term objectives, both for the user and the business. These systems are in their infancy in the industry and in need of practical solutions to some fundamental research challenges. At Adobe research, we have been implementing such systems for various use-cases, including points of interest recommendations, tutorial recommendations, next step guidance in multi-media editing software, and ad recommendation for optimizing lifetime value. There are many research challenges when building these systems, such as modeling the sequential behavior of users, deciding when to intervene and offer recommendations without annoying the user, evaluating policies offline with high confidence, safe deployment, non-stationarity, building systems from passive data that do not contain past recommendations, resource constraint optimization in multi-user systems, scaling to large and dynamic actions spaces, and handling and incorporating human cognitive biases. In this paper we cover various use-cases and research challenges we solved to make these systems practical.

In our previous work we have shown how Bayesian networks can be used for adaptive testing of student skills. Later, we have taken the advantage of monotonicity restrictions in order to learn models fitting data better. This article provides a synergy between these two phases as it evaluates Bayesian network models used for computerized adaptive testing and learned with a recently proposed monotonicity gradient algorithm. This learning method is compared with another monotone method, the isotonic regression EM algorithm. The quality of methods is empirically evaluated on a large data set of the Czech National Mathematics Exam. Besides advantages of adaptive testing approach we observed also advantageous behavior of monotonic methods, especially for small learning data set sizes. Another novelty of this work is the use of the reliability interval of the score distribution, which is used to predict student's final score and grade. In the experiments we have clearly shown we can shorten the test while keeping its reliability. We have also shown that the monotonicity increases the prediction quality with limited training data sets. The monotone model learned by the gradient method has a lower question prediction quality than unrestricted models but it is better in the main target of this application, which is the student score prediction. It is an important observation that a mere optimization of the model likelihood or the prediction accuracy do not necessarily lead to a model that describes best the student.

This paper presents an experimental comparison among four Automated Machine Learning (AutoML) methods for recommending the best classification algorithm for a given input dataset. Three of these methods are based on Evolutionary Algorithms (EAs), and the other is Auto-WEKA, a well-known AutoML method based on the Combined Algorithm Selection and Hyper-parameter optimisation (CASH) approach. The EA-based methods build classification algorithms from a single machine learning paradigm: either decision-tree induction, rule induction, or Bayesian network classification. Auto-WEKA combines algorithm selection and hyper-parameter optimisation to recommend classification algorithms from multiple paradigms. We performed controlled experiments where these four AutoML methods were given the same runtime limit for different values of this limit. In general, the difference in predictive accuracy of the three best AutoML methods was not statistically significant. However, the EA evolving decision-tree induction algorithms has the advantage of producing algorithms that generate interpretable classification models and that are more scalable to large datasets, by comparison with many algorithms from other learning paradigms that can be recommended by Auto-WEKA. We also observed that Auto-WEKA has shown meta-overfitting, a form of overfitting at the meta-learning level, rather than at the base-learning level.

We develop heuristic interpolation methods for the function $t \mapsto \operatorname{trace}\left( (\mathbf{A} + t \mathbf{B})^{-1} \right)$, where the matrices $\mathbf{A}$ and $\mathbf{B}$ are symmetric and positive definite and $t$ is a real variable. This function is featured in many applications in statistics, machine learning, and computational physics. The presented interpolation functions are based on the modification of a sharp upper bound that we derive for this function, which is a new trace inequality for matrices. We demonstrate the accuracy and performance of the proposed method with numerical examples, namely, the marginal maximum likelihood estimation for linear Gaussian process regression and the estimation of the regularization parameter of ridge regression with the generalized cross-validation method.

This paper proposes a novel fixed inducing points online Bayesian calibration (FIPO-BC) algorithm to efficiently learn the model parameters using a benchmark database. The standard Bayesian calibration (STD-BC) algorithm provides a statistical method to calibrate the parameters of computationally expensive models. However, the STD-BC algorithm scales very badly with the number of data points and lacks online learning capability. The proposed FIPO-BC algorithm greatly improves the computational efficiency and enables the online calibration by executing the calibration on a set of predefined inducing points. To demonstrate the procedure of the FIPO-BC algorithm, two tests are performed, finding the optimal value and exploring the posterior distribution of 1) the parameter in a simple function, and 2) the high-wave number damping factor in a scale-resolving turbulence model (SAS-SST). The results (such as the calibrated model parameter and its posterior distribution) of FIPO-BC with different inducing points are compared to those of STD-BC. It is found that FIPO-BC and STD-BC can provide very similar results, once the predefined set of inducing point in FIPO-BC is sufficiently fine. But, the FIPO-BC algorithm is at least ten times faster than the STD-BC algorithm. Meanwhile, the online feature of the FIPO-BC allows continuous updating of the calibration outputs and potentially reduces the workload on generating the database.

Reinforcement learning (RL) in episodic, factored Markov decision processes (FMDPs) is studied. We propose an algorithm called FMDP-BF, which leverages the factorization structure of FMDP. The regret of FMDP-BF is shown to be exponentially smaller than that of optimal algorithms designed for non-factored MDPs, and improves on the best previous result for FMDPs~\citep{osband2014near} by a factored of $\sqrt{H|\mathcal{S}_i|}$, where $|\mathcal{S}_i|$ is the cardinality of the factored state subspace and $H$ is the planning horizon. To show the optimality of our bounds, we also provide a lower bound for FMDP, which indicates that our algorithm is near-optimal w.r.t. timestep $T$, horizon $H$ and factored state-action subspace cardinality. Finally, as an application, we study a new formulation of constrained RL, known as RL with knapsack constraints (RLwK), and provides the first sample-efficient algorithm based on FMDP-BF.

We introduce a novel framework to account for sensitivity to rewards uncertainty in sequential decision-making problems. While risk-sensitive formulations for Markov decision processes studied so far focus on the distribution of the cumulative reward as a whole, we aim at learning policies sensitive to the uncertain/stochastic nature of the rewards, which has the advantage of being conceptually more meaningful in some cases. To this end, we present a new decomposition of the randomness contained in the cumulative reward based on the Doob decomposition of a stochastic process, and introduce a new conceptual tool - the \textit{chaotic variation} - which can rigorously be interpreted as the risk measure of the martingale component associated to the cumulative reward process. We innovate on the reinforcement learning side by incorporating this new risk-sensitive approach into model-free algorithms, both policy gradient and value function based, and illustrate its relevance on grid world and portfolio optimization problems.