The missing data problem has been broadly studied in the last few decades and has various applications in different areas such as statistics or bioinformatics. Even though many methods have been developed to tackle this challenge, most of those are imputation techniques that require multiple iterations through the data before yielding convergence. In addition, such approaches may introduce extra biases and noises to the estimated parameters. In this work, we propose novel algorithms to find the maximum likelihood estimates (MLEs) for a one-class/multiple-class randomly missing data set under some mild assumptions. As the computation is direct without any imputation, our algorithms do not require multiple iterations through the data, thus promising to be less time-consuming than other methods while maintaining superior estimation performance. We validate these claims by empirical results on various data sets of different sizes and release all codes in a GitHub repository to contribute to the research community related to this problem.

The shortcomings of maximum likelihood estimation in the context of model-based reinforcement learning have been highlighted by an increasing number of papers. When the model class is misspecified or has a limited representational capacity, model parameters with high likelihood might not necessarily result in high performance of the agent on a downstream control task. To alleviate this problem, we propose an end-to-end approach for model learning which directly optimizes the expected returns using implicit differentiation. We treat a value function that satisfies the Bellman optimality operator induced by the model as an implicit function of model parameters and show how to differentiate the function. We provide theoretical and empirical evidence highlighting the benefits of our approach in the model misspecification regime compared to likelihood-based methods.

In this article, we'll talk about Microsoft AI, the pathway to learn for beginners who are curious to explore the Microsoft AI Platforms, various functionalities and features supported by Machine Learning Studio in Azure, and the processes to train and better the Machine Learning Models with Azure. We also learn about different algorithms and thus gain the overall knowledge to get started and work with Microsoft Azure AI. Check out the official website of the summit to register as an attendee or to be a speaker and share your knowledge with the community. Microsoft AI is a powerful framework that enables organizations, researchers, and non-profits to use AI technologies with its powerful framework which offers services and features across domains of Machine Learning, Robotics, Data Science, IoT, and many more. One of the advantages of Azure can be realized with this example of how Machine Learning becomes more scalable in the Cloud even while working on Notebooks.

In this chapter, we investigate whether unique, optimal decision boundaries can be found. In order to do so, we first have to revisit several fundamental mathematical principles. Regularization is a mathematical tool, which allows us to find unique solutions even for highly ill-posed problems. In order to use this trick, we review norms and how they can be used to steer regression problems. Rosenblatt's Perceptron and Multi-Layer Perceptrons which are also called Artificial Neural Networks inherently suffer from this ill-posedness.

A general Bayesian framework is introduced for mixture modelling and inference with real-valued time series. At the top level, the state space is partitioned via the choice of a discrete context tree, so that the resulting partition depends on the values of some of the most recent samples. At the bottom level, a different model is associated with each region of the partition. This defines a very rich and flexible class of mixture models, for which we provide algorithms that allow for efficient, exact Bayesian inference. In particular, we show that the maximum a posteriori probability (MAP) model (including the relevant MAP context tree partition) can be precisely identified, along with its exact posterior probability. The utility of this general framework is illustrated in detail when a different autoregressive (AR) model is used in each state-space region, resulting in a mixture-of-AR model class. The performance of the associated algorithmic tools is demonstrated in the problems of model selection and forecasting on both simulated and real-world data, where they are found to provide results as good or better than state-of-the-art methods.

This paper investigates the theoretical and empirical performance of Fisher-Pitman-type permutation tests for assessing the equality of unknown Poisson mixture distributions. Building on nonparametric maximum likelihood estimators (NPMLEs) of the mixing distribution, these tests are theoretically shown to be able to adapt to complicated unspecified structures of count data and also consistent against their corresponding ANOVA-type alternatives; the latter is a result in parallel to classic claims made by Robinson (Robinson, 1973). The studied methods are then applied to a single-cell RNA-seq data obtained from different cell types from brain samples of autism subjects and healthy controls; empirically, they unveil genes that are differentially expressed between autism and control subjects yet are missed using common tests. For justifying their use, rate optimality of NPMLEs is also established in settings similar to nonparametric Gaussian (Wu and Yang, 2020a) and binomial mixtures (Tian et al., 2017; Vinayak et al., 2019).

We investigate the classical active pure exploration problem in Markov Decision Processes, where the agent sequentially selects actions and, from the resulting system trajectory, aims at identifying the best policy as fast as possible. We propose an information-theoretic lower bound on the average number of steps required before a correct answer can be given with probability at least $1-\delta$. This lower bound involves a non-convex optimization problem, for which we propose a convex relaxation. We further provide an algorithm whose sample complexity matches the relaxed lower bound up to a factor $2$. This algorithm addresses general communicating MDPs; we propose a variant with reduced exploration rate (and hence faster convergence) under an additional ergodicity assumption. This work extends previous results relative to the \emph{generative setting}~\cite{marjani2020adaptive}, where the agent could at each step observe the random outcome of any (state, action) pair. In contrast, we show here how to deal with the \emph{navigation constraints}. Our analysis relies on an ergodic theorem for non-homogeneous Markov chains which we consider of wide interest in the analysis of Markov Decision Processes.

Given a Markov decision process (MDP) and a linear-time ($\omega$-regular or LTL) specification, the controller synthesis problem aims to compute the optimal policy that satisfies the specification. More recently, problems that reason over the asymptotic behavior of systems have been proposed through the lens of steady-state planning. This entails finding a control policy for an MDP such that the Markov chain induced by the solution policy satisfies a given set of constraints on its steady-state distribution. This paper studies a generalization of the controller synthesis problem for a linear-time specification under steady-state constraints on the asymptotic behavior. We present an algorithm to find a deterministic policy satisfying $\omega$-regular and steady-state constraints by characterizing the solutions as an integer linear program, and experimentally evaluate our approach.

In practice, by simply training a generator and a discriminator together consisting of multi-layer neural networks with non-linear activation functions, using local search algorithms such as stochastic gradient descent ascent (SGDA), the generator network can be trained efficiently to generate samples from highly-complicated distributions (such as the distribution of images). Despite the great empirical success of GAN, it remains to be one of the least understood models on the theory side of deep learning. Most of existing theories focus on the statistical properties of GANs at the global-optimum [15, 16, 20, 87]. However, on the training side, gradient descent ascent only enjoys efficient convergence to a global optimum when the loss function is convex-concave, or efficient convergence to a critical point in general settings [37, 38, 48, 53, 71, 73, 75, 77, 78]. Due to the extreme non-linearity of the networks in both the generator and the discriminator, it is highly unlikely that the training objective of GANs can be convex-concave. In particular, even if the generator and the discriminator are linear functions over prescribed feature mappings-- such as the neural tangent kernel (NTK) feature mappings [3, 8, 9, 17, 18, 32, 35, 40, 41, 47, 51, 54, 65, 69, 92, 97] -- the training objective can still be non-convex-concave.

We introduce CAFLOW, a new diverse image-to-image translation model that simultaneously leverages the power of auto-regressive modeling and the modeling efficiency of conditional normalizing flows. We transform the conditioning image into a sequence of latent encodings using a multi-scale normalizing flow and repeat the process for the conditioned image. We model the conditional distribution of the latent encodings by modeling the auto-regressive distributions with an efficient multi-scale normalizing flow, where each conditioning factor affects image synthesis at its respective resolution scale. Our proposed framework performs well on a range of image-to-image translation tasks. It outperforms former designs of conditional flows because of its expressive auto-regressive structure.