Many systems are naturally modeled as Markov Decision Processes (MDPs), combining probabilities and strategic actions. Given a model of a system as an MDP and some logical specification of system behavior, the goal of synthesis is to find a policy that maximizes the probability of achieving this behavior. A popular choice for defining behaviors is Linear Temporal Logic (LTL). Policy synthesis on MDPs for properties specified in LTL has been well studied. LTL, however, is defined over infinite traces, while many properties of interest are inherently finite. Linear Temporal Logic over finite traces (LTLf) has been used to express such properties, but no tools exist to solve policy synthesis for MDP behaviors given finite-trace properties. We present two algorithms for solving this synthesis problem: the first via reduction of LTLf to LTL and the second using native tools for LTLf. We compare the scalability of these two approaches for synthesis and show that the native approach offers better scalability compared to existing automaton generation tools for LTL.

Bayesian nonparametrics based on completely random measures (CRMs) offers a flexible modeling approach when the number of clusters or latent components in a dataset is unknown. However, managing the infinite dimensionality of CRMs often leads to slow computation. Practical inference typically relies on either integrating out the infinite-dimensional parameter or using a finite approximation: a truncated finite approximation (TFA) or an independent finite approximation (IFA). The atom weights of TFAs are constructed sequentially, while the atoms of IFAs are independent, which (1) make them well-suited for parallel and distributed computation and (2) facilitates more convenient inference schemes. While IFAs have been developed in certain special cases in the past, there has not yet been a general template for construction or a systematic comparison to TFAs. We show how to construct IFAs for approximating distributions in a large family of CRMs, encompassing all those typically used in practice. We quantify the approximation error between IFAs and the target nonparametric prior, and prove that, in the worst-case, TFAs provide more component-efficient approximations than IFAs. However, in experiments on image denoising and topic modeling tasks with real data, we find that the error of Bayesian approximation methods overwhelms any finite approximation error, and IFAs perform very similarly to TFAs.

We consider online change detection of high dimensional data streams with sparse changes, where only a subset of data streams can be observed at each sensing time point due to limited sensing capacities. On the one hand, the detection scheme should be able to deal with partially observable data and meanwhile have efficient detection power for sparse changes. On the other, the scheme should be able to adaptively and actively select the most important variables to observe to maximize the detection power. To address these two points, in this paper, we propose a novel detection scheme called CDSSD. In particular, it describes the structure of high dimensional data with sparse changes by smooth-sparse decomposition, whose parameters can be learned via spike-slab variational Bayesian inference. Then the posterior Bayes factor, which incorporates the learned parameters and sparse change information, is formulated as a detection statistic. Finally, by formulating the statistic as the reward of a combinatorial multi-armed bandit problem, an adaptive sampling strategy based on Thompson sampling is proposed. The efficacy and applicability of our method in practice are demonstrated with numerical studies and a real case study.

Bayesian inference engines have become established as an important paradigm for inference in arbitrarily large and complex graphical models. Software platforms such as Infer.NET (Minka et al., 2018) and Stan (Carpenter et al., 2017) are instances of such Bayesian inference engines. They deliver approximate Bayesian inference, with varying degrees of inferential accuracy, by calling upon contemporary approaches such as expectation propagation, Hamiltonian Monte Carlo and variational approximation. The purpose of this short article is to show that effective and scalable probability density function estimation, or density estimation for short, can be achieved using Bayesian inference engines. We provide easy access for users of the R statistical computing environment (R Core Team, 2018) via a package named densEstBayes (Wand, 2020).

Supply and demand are two fundamental concepts of sellers and customers. Predicting demand accurately is critical for organizations in order to be able to make plans. In this paper, we propose a new approach for demand prediction on an e-commerce web site. The proposed model differs from earlier models in several ways. The business model used in the e-commerce web site, for which the model is implemented, includes many sellers that sell the same product at the same time at different prices where the company operates a market place model. The demand prediction for such a model should consider the price of the same product sold by competing sellers along the features of these sellers. In this study we first applied different regression algorithms for specific set of products of one department of a company that is one of the most popular online e-commerce companies in Turkey. Then we used stacked generalization or also known as stacking ensemble learning to predict demand. Finally, all the approaches are evaluated on a real world data set obtained from the e-commerce company. The experimental results show that some of the machine learning methods do produce almost as good results as the stacked generalization method.

Causal effect identification considers whether an interventional probability distribution can be uniquely determined from a passively observed distribution in a given causal structure. If the generating system induces context-specific independence (CSI) relations, the existing identification procedures and criteria based on do-calculus are inherently incomplete. We show that deciding causal effect non-identifiability is NP-hard in the presence of CSIs. Motivated by this, we design a calculus and an automated search procedure for identifying causal effects in the presence of CSIs. The approach is provably sound and it includes standard do-calculus as a special case. With the approach we can obtain identifying formulas that were unobtainable previously, and demonstrate that a small number of CSI-relations may be sufficient to turn a previously non-identifiable instance to identifiable.

Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments; productive changes manifest a moderate indeterminacy, but a large communicating effort with few productive changes characterize a chaotic environment. Hence, communicating, effective decision making and productive behavioral changes are related. The entropy measures the indeterminacy of the environment, and there is an entropy range in which communicating supports effective decision making. This conjecture is referred to here as the The Potential Productivity of Decisions. The computing engine that is causal to decision making should also have some indeterminacy. However, computations performed by standard Turing Machines are predetermined. To overcome this limitation an entropic mode of computing that is called here Relational-Indeterminate is presented. Its implementation in a table format has been used to model an associative memory. The present theory and experiment suggest the Entropy Trade-off: There is an entropy range in which computing is effective but if the entropy is too low computations are too rigid and if it is too high computations are unfeasible. The entropy trade-off of computing engines corresponds to the potential productivity of decisions of the environment. The theory is referred to an Interaction-Oriented Cognitive Architecture. Memory, perception, action and thought involve a level of indeterminacy and decision making may be free in such degree. The overall theory supports an ecological view of rationality. The entropy of the brain has been measured in neuroscience studies and the present theory supports that the brain is an entropic machine. The paper is concluded with a number of predictions that may be tested empirically.

Predicting undesirable events during the execution of a business process instance provides the process participants with an opportunity to intervene and keep the process aligned with its goals. Few approaches for tackling this challenge consider a multi-perspective view, where the flow perspective of the process is combined with its surrounding context. Given the many sources of data in today's world, context can vary widely and have various meanings. This paper addresses the issue of context being cause or effect of the next event and its impact on next event prediction. We leverage previous work on probabilistic models to develop a Dynamic Bayesian Network technique. Probabilistic models are considered comprehensible and they allow the end-user and his or her understanding of the domain to be involved in the prediction. Our technique models context attributes that have either a cause or effect relationship towards the event. We evaluate our technique with two real-life data sets and benchmark it with other techniques from the field of predictive process monitoring. The results show that our solution achieves superior prediction results if context information is correctly introduced into the model.

We propose a general framework to robustly characterize joint and conditional probability distributions via transport maps. Transport maps or "flows" deterministically couple two distributions via an expressive monotone transformation. Yet, learning the parameters of such transformations in high dimensions is challenging given few samples from the unknown target distribution, and structural choices for these transformations can have a significant impact on performance. Here we formulate a systematic framework for representing and learning monotone maps, via invertible transformations of smooth functions, and demonstrate that the associated minimization problem has a unique global optimum. Given a hierarchical basis for the appropriate function space, we propose a sample-efficient adaptive algorithm that estimates a sparse approximation for the map. We demonstrate how this framework can learn densities with stable generalization performance across a wide range of sample sizes on real-world datasets.

We propose a generative Causal Adversarial Network (CAN) for learning and sampling from conditional and interventional distributions. In contrast to the existing CausalGAN which requires the causal graph to be given, our proposed framework learns the causal relations from the data and generates samples accordingly. The proposed CAN comprises a two-fold process namely Label Generation Network (LGN) and Conditional Image Generation Network (CIGN). The LGN is a GAN-based architecture which learns and samples from the causal model over labels. The sampled labels are then fed to CIGN, a conditional GAN architecture, which learns the relationships amongst labels and pixels and pixels themselves and generates samples based on them. This framework is equipped with an intervention mechanism which enables. the model to generate samples from interventional distributions. We quantitatively and qualitatively assess the performance of CAN and empirically show that our model is able to generate both interventional and conditional samples without having access to the causal graph for the application of face generation on CelebA data.