The concept of causality has a controversial history. The question of whether it is possible to represent and address causal problems with probability theory, or if fundamentally new mathematics such as the do calculus is required has been hotly debated, e.g. Pearl (2001) states "the building blocks of our scientific and everyday knowledge are elementary facts such as "mud does not cause rain" and "symptoms do not cause disease" and those facts, strangely enough, cannot be expressed in the vocabulary of probability calculus". This has lead to a dichotomy between advocates of causal graphical modeling and the do calculus, and researchers applying Bayesian methods. In this paper we demonstrate that, while it is critical to explicitly model our assumptions on the impact of intervening in a system, provided we do so, estimating causal effects can be done entirely within the standard Bayesian paradigm. The invariance assumptions underlying causal graphical models can be encoded in ordinary Probabilistic graphical models, allowing causal estimation with Bayesian statistics, equivalent to the do calculus. Elucidating the connections between these approaches is a key step toward enabling the insights provided by each to be combined to solve real problems.

It is common practice in using regression type models for inferring causal effects, that inferring the correct causal relationship requires extra covariates are included or ``adjusted for''. Without performing this adjustment erroneous causal effects can be inferred. Given this phenomenon it is common practice to include as many covariates as possible, however such advice comes unstuck in the presence of M-bias. M-Bias is a problem in causal inference where the correct estimation of treatment effects requires that certain variables are not adjusted for i.e. are simply neglected from inclusion in the model. This issue caused a storm of controversy in 2009 when Rubin, Pearl and others disagreed about if it could be problematic to include additional variables in models when inferring causal effects. This paper makes two contributions to this issue. Firstly we provide a Bayesian solution to the M-Bias problem. The solution replicates Pearl's solution, but consistent with Rubin's advice we condition on all variables. Secondly the fact that we are able to offer a solution to this problem in Bayesian terms shows that it is indeed possible to represent causal relationships within the Bayesian paradigm, albeit in an extended space. We make several remarks on the similarities and differences between causal graphical models which implement the do-calculus and probabilistic graphical models which enable Bayesian statistics. We hope this work will stimulate more research on unifying Pearl's causal calculus using causal graphical models with traditional Bayesian statistics and probabilistic graphical models.

This article describes REBA, a knowledge representation and reasoning architecture for robots that is based on tightly-coupled transition diagrams of the domain at two different levels of granularity. An action language is extended to support non-boolean fluents and non-deterministic causal laws, and used to describe the domain's transition diagrams, with the fine-resolution transition diagram being defined as a refinement of the coarse-resolution transition diagram. The coarse-resolution system description, and a history that includes prioritized defaults, are translated into an Answer Set Prolog (ASP) program. For any given goal, inference in the ASP program provides a plan of abstract actions. To implement each such abstract action, the robot automatically zooms to the part of the fine-resolution transition diagram relevant to this action. The zoomed fine-resolution system description, and a probabilistic representation of the uncertainty in sensing and actuation, are used to construct a partially observable Markov decision process (POMDP). The policy obtained by solving the POMDP is invoked repeatedly to implement the abstract action as a sequence of concrete actions. The fine-resolution outcomes of executing these concrete actions are used to infer coarse-resolution outcomes that are added to the coarse-resolution history and used for subsequent coarse-resolution reasoning. The architecture thus combines the complementary strengths of declarative programming and probabilistic graphical models to represent and reason with non-monotonic logic-based and probabilistic descriptions of uncertainty and incomplete domain knowledge. In addition, we describe a general methodology for the design of software components of a robot based on these knowledge representation and reasoning tools, and provide a path for proving the correctness of these components. The architecture is evaluated in simulation and on a mobile robot finding and moving target objects to desired locations in indoor domains, to show that the architecture supports reliable and efficient reasoning with violation of defaults, noisy observations and unreliable actions, in complex domains.

As Machine Learning (ML) becomes pervasive in various real world systems, the need for models to be interpretable or explainable has increased. We focus on interpretability, noting that models often need to be constrained in size for them to be considered understandable, e.g., a decision tree of depth 5 is easier to interpret than one of depth 50. This suggests a trade-off between interpretability and accuracy. We propose a technique to minimize this tradeoff. Our strategy is to first learn a powerful, possibly black-box, probabilistic model on the data, which we refer to as the oracle. We use this to adaptively sample the training dataset to present data to our model of interest to learn from. Determining the sampling strategy is formulated as an optimization problem that, independent of the dimensionality of the data, uses only seven variables. We empirically show that this often significantly increases the accuracy of our model. Our technique is model agnostic - in that, both the interpretable model and the oracle might come from any model family. Results using multiple real world datasets, using Linear Probability Models and Decision Trees as interpretable models, and Gradient Boosted Model and Random Forest as oracles are presented. Additionally, we discuss an interesting example of using a sentence-embedding based text classifier as an oracle to improve the accuracy of a term-frequency based bag-of-words linear classifier.

We introduce a framework for approximate analysis of Markov decision processes (MDP) with bounded-, unbounded-, and infinite-horizon properties. The main idea is to identify a ``core'' of an MDP, i.e., a subsystem where we provably remain with high probability, and to avoid computation on the less relevant rest of the state space. Although we identify the core using simulations and statistical techniques, it allows for rigorous error bounds in the analysis. Consequently, we obtain efficient analysis algorithms based on partial exploration for various settings, including the challenging case of strongly connected systems.

According to Thomas Edison, g, for example a fragrance composed of 700 g of "ingredient "Genius is one percent inspiration and 99 percent A" and 300 g of "ingredient B". A fragrance can have desired perspiration" is an example. In many situations, properties related to aromatics (e.g., the type of smell), researchers and inventors already have a variety popularity (e.g., frequent patterns of ingredient combinations, of data and manage to create something new or combinations that should be avoided), and appropriateness by using it, but the key problem is how to select for certain use cases (e.g., combinations for perfumes, shampoos, and combine knowledge. In this paper, we propose or hand soaps). Perfumers who create new fragrances a new Markov chain Monte Carlo (MCMC) algorithm seek to develop various fragrances with desired properties. It to generate composition ratios, nonnegativeinteger-valued is also possible that perfumers are willing to accept certain vectors with two properties: (i) the fragrances lacking some desired properties, because they can sum of the elements of each vector is constant, and still draw inspiration from such fragrances. Thus, it is interesting (ii) only a small number of elements is nonzero.

Machine learning develops rapidly, which has made many theoretical breakthroughs and is widely applied in various fields. Optimization, as an important part of machine learning, has attracted much attention of researchers. With the exponential growth of data amount and the increase of model complexity, optimization methods in machine learning face more and more challenges. A lot of work on solving optimization problems or improving optimization methods in machine learning has been proposed successively. The systematic retrospect and summary of the optimization methods from the perspective of machine learning are of great significance, which can offer guidance for both developments of optimization and machine learning research. In this paper, we first describe the optimization problems in machine learning. Then, we introduce the principles and progresses of commonly used optimization methods. Next, we summarize the applications and developments of optimization methods in some popular machine learning fields. Finally, we explore and give some challenges and open problems for the optimization in machine learning.

We study the problem of learning graphical models with latent variables. We give the first algorithm for learning locally consistent (ferromagnetic or antiferromagnetic) Restricted Boltzmann Machines (or RBMs) with {\em arbitrary} external fields. Our algorithm has optimal dependence on dimension in the sample complexity and run time however it suffers from a sub-optimal dependency on the underlying parameters of the RBM. Prior results have been established only for {\em ferromagnetic} RBMs with {\em consistent} external fields (signs must be same)\cite{bresler2018learning}. The proposed algorithm strongly relies on the concavity of magnetization which does not hold in our setting. We show the following key structural property: even in the presence of arbitrary external field, for any two observed nodes that share a common latent neighbor, the covariance is high. This enables us to design a simple greedy algorithm that maximizes covariance to iteratively build the neighborhood of each vertex.

Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data, which has received the most attention in the literature, in this paper we will review how Bayesian networks can model dynamic data and data with incomplete observations. Such data are the norm at the forefront of research and applications, and Bayesian networks are uniquely positioned to model them due to their explainability and interpretability.

If you're anything like my dad, you've worked in IT for decades but have only tangentially touched data science. Now, your new C-something-O wants you to fire up a data analytics team and work with new a set of buzzwords you've only vaguely heard about at conferences. Or perhaps you're a developer at a fast-moving startup and have spent weeks finalizing an algorithm, only to be stymied by issues with deploying the model onto your web application for real time use. For both cases, H2O.ai is definitely a solution worth looking into. H2O.ai positions itself as a software package that streamlines the machine learning process through its open source package H2O and AutoML.