After the user provides a few examples of desired outcomes, MURAL automatically infers a reward function that takes into account these examples and the agent's uncertainty for each state. Although reinforcement learning has shown success in domains such as robotics, chip placement and playing video games, it is usually intractable in its most general form. In particular, deciding when and how to visit new states in the hopes of learning more about the environment can be challenging, especially when the reward signal is uninformative. These questions of reward specification and exploration are closely connected -- the more directed and "well shaped" a reward function is, the easier the problem of exploration becomes. The answer to the question of how to explore most effectively is likely to be closely informed by the particular choice of how we specify rewards.

Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen set of time horizons, e.g. Brier score (BS) and Bernoulli log likelihood (BLL). Models trained with maximum likelihood may have poor BS or BLL since maximum likelihood does not directly optimize these criteria. Directly optimizing criteria like BS requires inverse-weighting by the censoring distribution, estimation of which itself also requires inverse-weighted by the failure distribution. But neither are known. To resolve this dilemma, we introduce Inverse-Weighted Survival Games to train both failure and censoring models with respect to criteria such as BS or BLL. In these games, objectives for each model are built from re-weighted estimates featuring the other model, where the re-weighting model is held fixed during training. When the loss is proper, we show that the games always have the true failure and censoring distributions as a stationary point. This means models in the game do not leave the correct distributions once reached. We construct one case where this stationary point is unique. We show that these games optimize BS on simulations and then apply these principles on real world cancer and critically-ill patient data.

We consider the problem of learning a sparse undirected graph underlying a given set of multivariate data. We focus on graph Laplacian-related constraints on the sparse precision matrix that encodes conditional dependence between the random variables associated with the graph nodes. Under these constraints the off-diagonal elements of the precision matrix are non-positive (total positivity), and the precision matrix may not be full-rank. We investigate modifications to widely used penalized log-likelihood approaches to enforce total positivity but not the Laplacian structure. The graph Laplacian can then be extracted from the off-diagonal precision matrix. An alternating direction method of multipliers (ADMM) algorithm is presented and analyzed for constrained optimization under Laplacian-related constraints and lasso as well as adaptive lasso penalties. Numerical results based on synthetic data show that the proposed constrained adaptive lasso approach significantly outperforms existing Laplacian-based approaches. We also evaluate our approach on real financial data.

We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso-based frequency-domain formulation of the problem based on frequency-domain sufficient statistic for the observed time series is presented. We investigate an alternating direction method of multipliers (ADMM) approach for optimization of the sparse-group lasso penalized log-likelihood. We provide sufficient conditions for convergence in the Frobenius norm of the inverse PSD estimators to the true value, jointly across all frequencies, where the number of frequencies are allowed to increase with sample size. This results also yields a rate of convergence. We also empirically investigate selection of the tuning parameters based on Bayesian information criterion, and illustrate our approach using numerical examples utilizing both synthetic and real data.

We consider the problem of simulating diffusion bridges, i.e. diffusion processes that are conditioned to initialize and terminate at two given states. Diffusion bridge simulation has applications in diverse scientific fields and plays a crucial role for statistical inference of discretely-observed diffusions. This is known to be a challenging problem that has received much attention in the last two decades. In this work, we first show that the time-reversed diffusion bridge process can be simulated if one can time-reverse the unconditioned diffusion process. We introduce a variational formulation to learn this time-reversal that relies on a score matching method to circumvent intractability. We then consider another iteration of our proposed methodology to approximate the Doob's $h$-transform defining the diffusion bridge process. As our approach is generally applicable under mild assumptions on the underlying diffusion process, it can easily be used to improve the proposal bridge process within existing methods and frameworks. We discuss algorithmic considerations and extensions, and present some numerical results.

Artificial Intelligence (AI) algorithms are increasingly providing decision making and operational support across multiple domains. AI includes a wide library of algorithms for different problems. One important notion for the adoption of AI algorithms into operational decision process is the concept of assurance. The literature on assurance, unfortunately, conceals its outcomes within a tangled landscape of conflicting approaches, driven by contradicting motivations, assumptions, and intuitions. Accordingly, albeit a rising and novel area, this manuscript provides a systematic review of research works that are relevant to AI assurance, between years 1985 - 2021, and aims to provide a structured alternative to the landscape. A new AI assurance definition is adopted and presented and assurance methods are contrasted and tabulated. Additionally, a ten-metric scoring system is developed and introduced to evaluate and compare existing methods. Lastly, in this manuscript, we provide foundational insights, discussions, future directions, a roadmap, and applicable recommendations for the development and deployment of AI assurance.

This formula was devised and penned by respected Thomas Bayes, renowned statistician.It is an arithmetical formula for determining conditional probability. Conditional probability is the likelihood of an outcome occurring, based on a previous outcome occurring. This might be a bit brain-teasing as you are working backwards. Bayes' theorem may be derived from the definition of conditional probability, P(Do not launch Stock price increases) 0.4 0.30 0.12 Thus, there is a 57% probability that the company's share price will increase. Bayes' Theorem has several forms.

Hamiltonian Monte Carlo (HMC) methods are widely used to draw samples from unnormalized target densities due to high efficiency and favorable scalability with respect to increasing space dimensions. However, HMC struggles when the target distribution is multimodal, because the maximum increase in the potential energy function (i.e., the negative log density function) along the simulated path is bounded by the initial kinetic energy, which follows a half of the $\chi_d^2$ distribution, where d is the space dimension. In this paper, we develop a Hamiltonian Monte Carlo method where the constructed paths can travel across high potential energy barriers. This method does not require the modes of the target distribution to be known in advance. Our approach enables frequent jumps between the isolated modes of the target density by continuously varying the mass of the simulated particle while the Hamiltonian path is constructed. Thus, this method can be considered as a combination of HMC and the tempered transitions method. Compared to other tempering methods, our method has a distinctive advantage in the Gibbs sampler settings, where the target distribution changes at each step. We develop a practical tuning strategy for our method and demonstrate that it can construct globally mixing Markov chains targeting high-dimensional, multimodal distributions, using mixtures of normals and a sensor network localization problem.

Meta-, multi-task, and federated learning can be all viewed as solving similar tasks, drawn from an unknown distribution that reflects task similarities. In this work, we provide a unified view of all these problems, as learning to act in a hierarchical Bayesian bandit. We analyze a natural hierarchical Thompson sampling algorithm (hierTS) that can be applied to any problem in this class. Our regret bounds hold under many instances of such problems, including when the tasks are solved sequentially or in parallel; and capture the structure of the problems, such that the regret decreases with the width of the task prior. Our proofs rely on novel total variance decompositions, which can be applied to other graphical model structures. Finally, our theory is complemented by experiments, which show that the hierarchical structure helps with knowledge sharing among the tasks. This confirms that hierarchical Bayesian bandits are a universal and statistically-efficient tool for learning to act with similar bandit tasks.

Across many data domains, co-occurrence statistics about the joint appearance of objects are powerfully informative. By transforming unsupervised learning problems into decompositions of co-occurrence statistics, spectral algorithms provide transparent and efficient algorithms for posterior inference such as latent topic analysis and community detection. As object vocabularies grow, however, it becomes rapidly more expensive to store and run inference algorithms on co-occurrence statistics. Rectifying co-occurrence, the key process to uphold model assumptions, becomes increasingly more vital in the presence of rare terms, but current techniques cannot scale to large vocabularies. We propose novel methods that simultaneously compress and rectify co-occurrence statistics, scaling gracefully with the size of vocabulary and the dimension of latent space. We also present new algorithms learning latent variables from the compressed statistics, and verify that our methods perform comparably to previous approaches on both textual and non-textual data.