Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate scalable sampling-based posterior inference by exploitation of the combinatorial structure of the factor conditionals. Maximum a posteriori decompositions feature higher accuracies than existing techniques throughout a wide range of simulated conditions. Moreover, the probabilistic approach facilitates the treatment of missing data and enables model selection with much greater accuracy. We investigate three real-world data-sets. First, temporal interaction networks in a hospital ward and behavioural data of university students demonstrate the inference of instructive latent patterns. Next, we decompose a tensor with more than 10 billion data points, indicating relations of gene expression in cancer patients. Not only does this demonstrate scalability, it also provides an entirely novel perspective on relational properties of continuous data and, in the present example, on the molecular heterogeneity of cancer. Our implementation is available on GitHub: https://github.com/TammoR/LogicalFactorisationMachines.

Abstract--In recent years, reinforcement learning has achieved many remarkable successes due to the growing adoption of deep learning techniques and the rapid growth in computing power . Nevertheless, it is well-known that flat reinforcement learning algorithms are often not able to learn well and data-efficient in tasks having hierarchical structures, e.g. Hierarchical reinforcement learning is a principled approach that is able to tackle these challenging tasks. On the other hand, many real-world tasks usually have only partial observability in which state measurements are often imperfect and partially observable. The problems of RL in such settings can be formulated as a partially observable Markov decision process (POMDP). In this paper, we study hierarchical RL in POMDP in which the tasks have only partial observability and possess hierarchical properties. We propose a hierarchical deep reinforcement learning approach for learning in hierarchical POMDP . The deep hierarchical RL algorithm is proposed to apply to both MDP and POMDP learning. We evaluate the proposed algorithm on various challenging hierarchical POMDP . Reinforcement Learning (RL) [1] is a subfield of machine learning focused on learning a policy in order to maximize total cumulative reward in an unknown environment. RL is divided into two approaches: value-based approach and policy-based approach [15]. A typical value-based approach tries to obtain an optimal policy by finding optimal value functions. The value functions are updated using the immediate reward and the discounted value of the next state. Some methods based on this approach are Q-learning, SARSA, and TD-learning [1]. In contrast, the policy-based approach directly learns a parameterized policy that maximizes the cumulative discounted reward.

The study of ML algorithms has gained immense traction post the Harvard Business Review article terming a'Data Scientist' as the'Sexiest job of the 21st century'. So, for those starting out in the field of ML, we decided to do a reboot of our immensely popular Gold blog The 10 Algorithms Machine Learning Engineers need to know -- albeit this post is targeted towards beginners. ML algorithms are those that can learn from data and improve from experience, without human intervention. Learning tasks may include learning the function that maps the input to the output, learning the hidden structure in unlabeled data; or'instance-based learning', where a class label is produced for a new instance by comparing the new instance (row) to instances from the training data, which were stored in memory. 'Instance-based learning' does not create an abstraction from specific instances. Supervised learning can be explained as follows: use labeled training data to learn the mapping function from the input variables (X) to the output variable (Y).

Data Science has become the new desirable IT job. While there are only few in the market conversant with the terms like python, machine learning, deep learning and transflow, it is also a fact that these skills are high in demand. Acadgild will transform you into a Data Scientist by delivering hands-on experience in Statistics, Machine Learning, Deep Learning and Artificial Intelligence (AI) using Python, TensorFlow, Apache Spark, R and Tableau. The course provides in-depth understanding of Machine Learning and Deep Learning algorithms such as Linear Regression, Logistic Regression, Naive Bayes Classifiers, Decision Tree and Random Forest, Support Vector Machine, Artificial Neural Networks and more. This 24 weeks long Data Science course has several advantages like 400 total coding hours and experienced industry mentors.

Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application, and therefore cannot guarantee optimal predictions for a given task. To make more suitable task-specific approximations, we introduce a new loss-calibrated evidence lower bound for Bayesian neural networks in the context of supervised learning, informed by Bayesian decision theory. By introducing a lower bound that depends on a utility function, we ensure that our approximation achieves higher utility than traditional methods for applications that have asymmetric utility functions. Furthermore, in using dropout inference, we highlight that our new objective is identical to that of standard dropout neural networks, with an additional utility-dependent penalty term. We demonstrate our new loss-calibrated model with an illustrative medical example and a restricted model capacity experiment, and highlight failure modes of the comparable weighted cross entropy approach. Lastly, we demonstrate the scalability of our method to real world applications with per-pixel semantic segmentation on an autonomous driving data set.

Online reviews play an important role in influencing buyers' daily purchase decisions. However, fake and meaningless reviews, which cannot reflect users' genuine purchase experience and opinions, widely exist on the Web and pose great challenges for users to make right choices. Therefore,it is desirable to build a fair model that evaluates the quality of products by distinguishing spamming reviews. We present an end-to-end trainable unified model to leverage the appealing properties from Autoencoder and random forest. A stochastic decision tree model is implemented to guide the global parameter learning process. Extensive experiments were conducted on a large Amazon review dataset. The proposed model consistently outperforms a series of compared methods.

Modeling and verifying real-world cyber-physical systems is challenging, which is especially so for complex systems where manually modeling is infeasible. In this work, we report our experience on combining model learning and abstraction refinement to analyze a challenging system, i.e., a real-world Secure Water Treatment system (SWaT). Given a set of safety requirements, the objective is to either show that the system is safe with a high probability (so that a system shutdown is rarely triggered due to safety violation) or not. As the system is too complicated to be manually modeled, we apply latest automatic model learning techniques to construct a set of Markov chains through abstraction and refinement, based on two long system execution logs (one for training and the other for testing). For each probabilistic safety property, we either report it does not hold with a certain level of probabilistic confidence, or report that it holds by showing the evidence in the form of an abstract Markov chain. The Markov chains can subsequently be implemented as runtime monitors in SWaT.

Planning robust executions under uncertainty is a fundamental challenge for building autonomous robots. Partially Observable Markov Decision Processes (POMDPs) provide a standard framework for modeling uncertainty in many applications. In this work, we study POMDPs with safe-reachability objectives, which require that with a probability above some threshold, a goal state is eventually reached while keeping the probability of visiting unsafe states below some threshold. This POMDP formulation is different from the traditional POMDP models with optimality objectives and we show that in some cases, POMDPs with safe-reachability objectives can provide a better guarantee of both safety and reachability than the existing POMDP models through an example. A key algorithmic problem for POMDPs is policy synthesis, which requires reasoning over a vast space of beliefs (probability distributions). To address this challenge, we introduce the notion of a goal-constrained belief space, which only contains beliefs reachable from the initial belief under desired executions that can achieve the given safe-reachability objective. Our method compactly represents this space over a bounded horizon using symbolic constraints, and employs an incremental Satisfiability Modulo Theories (SMT) solver to efficiently search for a valid policy over it. We evaluate our method using a case study involving a partially observable robotic domain with uncertain obstacles. The results show that our method can synthesize policies over large belief spaces with a small number of SMT solver calls by focusing on the goal-constrained belief space.

We introduce a new class of identifiable DAG models, where each node has a conditional distribution given its parents belongs to a family of generalized hypergeometric distributions (GHD). a family of generalized hypergeometric distributions (GHD) includes a lot of discrete distributions such as Binomial, Beta-binomial, Poisson, Poisson type, displaced Poisson, hyper-Poisson, logarithmic, and many more. We prove that if the data drawn from the new class of DAG models, one can fully identify the graph. We further provide a reliable and tractable algorithm that recovers the directed graph from finitely many data. We show through theoretical results and simulations that our algorithm is statistically consistent even in high-dimensional settings ($n >p$) if the degree of the graph is bounded, and performs well compared to state-of-the-art DAG-learning algorithms.

Our article shows how to carry out Bayesian inference by combining data subsampling with Sequential Monte Carlo (SMC). This takes advantage of the attractive properties of SMC for Bayesian computations with the ability of subsampling to tackle big data problems. SMC sequentially updates a cloud of particles through a sequence of densities, beginning with a density that is easy to sample from such as the prior and ending with the posterior density. Each update of the particle cloud consists of three steps: reweighting, resampling, and moving. In the move step, each particle is moved using a Markov kernel and this is typically the most computationally expensive part, particularly when the dataset is large. It is crucial to have an efficient move step to ensure particle diversity. Our article makes two important contributions. First, in order to speed up the SMC computation, we use an approximately unbiased and efficient annealed likelihood estimator based on data subsampling. The subsampling approach is more memory efficient than the corresponding full data SMC, which is a great advantage for parallel computation. Second, we use a Metropolis within Gibbs kernel with two conditional updates. First, a Hamiltonian Monte Carlo update makes distant moves for the model parameters. Second, a block pseudo-marginal proposal is used for the particles corresponding to the auxiliary variables for the data subsampling. We demonstrate the usefulness of the methodology using two large datasets.