**Mixed Markov Models (MMM)**

Markov random fields can encode complex probabilistic relationships involving multiple variables and admit efficient procedures for probabilistic inference. However, from a knowledge engineering point of view, these models suffer from a serious limitation. The graph of a Markov field must connect all pairs of variables that are conditionally dependent even for a single choice of values of the other variables. This makes it hard to encode interactions that occur only in a certain context and are absent in all others. Furthermore, the requirement that two variables be connected unless always conditionally independent may lead to excessively dense graphs, obscuring the independencies present among the variables and leading to computationally prohibitive inference algorithms. Mumford proposed an alternative modeling framework where the graph need not be rigid and completely determined a priori. Mixed Markov models contain node-valued random variables that, when instantiated, augment the graph by a set of transient edges. A single joint probability distribution relates the values of regular and node-valued variables. In this article, we study the analytical and computational properties of mixed Markov models. In particular, we show that positive mixed models have a local Markov property that is equivalent to their global factorization. We also describe a computationally efficient procedure for answering probabilistic queries in mixed Markov models. … **Maximum Margin Interval Trees**

Learning a regression function using censored or interval-valued output data is an important problem in fields such as genomics and medicine. The goal is to learn a real-valued prediction function, and the training output labels indicate an interval of possible values. Whereas most existing algorithms for this task are linear models, in this paper we investigate learning nonlinear tree models. We propose to learn a tree by minimizing a margin-based discriminative objective function, and we provide a dynamic programming algorithm for computing the optimal solution in log-linear time. We show empirically that this algorithm achieves state-of-the-art speed and prediction accuracy in a benchmark of several data sets. … **Online Multi-Armed Bandit**

We introduce a novel variant of the multi-armed bandit problem, in which bandits are streamed one at a time to the player, and at each point, the player can either choose to pull the current bandit or move on to the next bandit. Once a player has moved on from a bandit, they may never visit it again, which is a crucial difference between our problem and classic multi-armed bandit problems. In this online context, we study Bernoulli bandits (bandits with payout Ber($p_i$) for some underlying mean $p_i$) with underlying means drawn i.i.d. from various distributions, including the uniform distribution, and in general, all distributions that have a CDF satisfying certain differentiability conditions near zero. In all cases, we suggest several strategies and investigate their expected performance. Furthermore, we bound the performance of any optimal strategy and show that the strategies we have suggested are indeed optimal up to a constant factor. We also investigate the case where the distribution from which the underlying means are drawn is not known ahead of time. We again, are able to suggest algorithms that are optimal up to a constant factor for this case, given certain mild conditions on the universe of distributions. …

# If you did not already know

**09**
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Jun 2018

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