Bayesian statistics is all about belief. We have some prior belief about the true model, and we combine that with the likelihood of our data to get our posterior belief about the true model. In some cases, we have knowledge about our domain before we see any of the data. Bayesian inference provides a straightforward way to encode that belief into a prior probability distribution. For example, say I am an economist predicting the effects of interest rates on tech stock price changes.

Weak lensing mass-mapping is a useful tool to access the full distribution of dark matter on the sky, but because of intrinsic galaxy ellipticies and finite fields/missing data, the recovery of dark matter maps constitutes a challenging ill-posed inverse problem. We introduce a novel methodology allowing for efficient sampling of the high-dimensional Bayesian posterior of the weak lensing mass-mapping problem, and relying on simulations for defining a fully non-Gaussian prior. We aim to demonstrate the accuracy of the method on simulations, and then proceed to applying it to the mass reconstruction of the HST/ACS COSMOS field. The proposed methodology combines elements of Bayesian statistics, analytic theory, and a recent class of Deep Generative Models based on Neural Score Matching. This approach allows us to do the following: 1) Make full use of analytic cosmological theory to constrain the 2pt statistics of the solution. 2) Learn from cosmological simulations any differences between this analytic prior and full simulations. 3) Obtain samples from the full Bayesian posterior of the problem for robust Uncertainty Quantification. We demonstrate the method on the $\kappa$TNG simulations and find that the posterior mean significantly outperfoms previous methods (Kaiser-Squires, Wiener filter, Sparsity priors) both on root-mean-square error and in terms of the Pearson correlation. We further illustrate the interpretability of the recovered posterior by establishing a close correlation between posterior convergence values and SNR of clusters artificially introduced into a field. Finally, we apply the method to the reconstruction of the HST/ACS COSMOS field and yield the highest quality convergence map of this field to date.

We propose a reinforcement learning (RL) approach to compute the expression of quasi-stationary distribution. Based on the fixed-point formulation of quasi-stationary distribution, we minimize the KL-divergence of two Markovian path distributions induced by the candidate distribution and the true target distribution. To solve this challenging minimization problem by gradient descent, we apply the reinforcement learning technique by introducing the reward and value functions. We derive the corresponding policy gradient theorem and design an actor-critic algorithm to learn the optimal solution and the value function. The numerical examples of finite state Markov chain are tested to demonstrate the new method.

While such single-timestep explanations produce valuable insight, they lack any representation We introduce a data-driven, model-agnostic technique of the dynamics that differentiate control from other learning for generating a human-interpretable summary domains. A complementary direction for explaining agent of the salient points of contrast within an behaviour would be to facilitate human understanding of the evolving dynamical system, such as the learning dynamics over two timescales: (1) short-term sequences of process of a control agent. It involves the aggregation state transitions ("when you go here, what happens next?") of transition data along both spatial and and (2) long-term trends in policy evolution ("what did you temporal dimensions according to an informationtheoretic do in the past, and when, how and why did that change?").

In a cooperative multiagent system, a collection of agents executes a joint policy in order to achieve some common objective. The successful deployment of such systems hinges on the availability of reliable inter-agent communication. However, many sources of potential disruption to communication exist in practice, such as radio interference, hardware failure, and adversarial attacks. In this work, we develop joint policies for cooperative multiagent systems that are robust to potential losses in communication. More specifically, we develop joint policies for cooperative Markov games with reach-avoid objectives. First, we propose an algorithm for the decentralized execution of joint policies during periods of communication loss. Next, we use the total correlation of the state-action process induced by a joint policy as a measure of the intrinsic dependencies between the agents. We then use this measure to lower-bound the performance of a joint policy when communication is lost. Finally, we present an algorithm that maximizes a proxy to this lower bound in order to synthesize minimum-dependency joint policies that are robust to communication loss. Numerical experiments show that the proposed minimum-dependency policies require minimal coordination between the agents while incurring little to no loss in performance; the total correlation value of the synthesized policy is one fifth of the total correlation value of the baseline policy which does not take potential communication losses into account. As a result, the performance of the minimum-dependency policies remains consistently high regardless of whether or not communication is available. By contrast, the performance of the baseline policy decreases by twenty percent when communication is lost.

As a measure of the long-term contribution produced by customers in a service or product relationship, life-time value, or LTV, can more comprehensively find the optimal strategy for service delivery. However, it is challenging to accurately abstract the LTV scene, model it reasonably, and find the optimal solution. The current theories either cannot precisely express LTV because of the single modeling structure, or there is no efficient solution. We propose a general LTV modeling method, which solves the problem that customers' long-term contribution is difficult to quantify while existing methods, such as modeling the click-through rate, only pursue the short-term contribution. At the same time, we also propose a fast dynamic programming solution based on a mutated bisection method and the memoryless repeated experiments assumption. The model and method can be applied to different service scenarios, such as the recommendation system. Experiments on real-world datasets confirm the effectiveness of the proposed model and optimization method. In addition, this whole LTV structure was deployed at a large E-commerce mobile phone application, where it managed to select optimal push message sending time and achieved a 10\% LTV improvement.

Supervised classification techniques use training samples to learn a classification rule with small expected 0-1-loss(error probability). Conventional methods enable tractable learning and provide out-of-sample generalization by using surrogate losses instead of the 0-1-loss and considering specific families of rules (hypothesis classes). This paper presents minimax risk classifiers (MRCs) that minimize the worst-case 0-1-loss over general classification rules and provide tight performance guarantees at learning. We show that MRCs are strongly universally consistent using feature mappings given by characteristic kernels. The paper also proposes efficient optimization techniques for MRC learning and shows that the methods presented can provide accurate classification together with tight performance guarantees.

Artificial neural networks (ANNs) providing sophisticated, power-efficient classification are finding their way into thin-film electronics. Thin-film technologies require robust, layout-efficient devices with facile manufacturability. Here, we show how the multimodal transistor’s (MMT’s) transfer characteristic, with linear dependence in saturation, replicates the rectified linear unit (ReLU) activation function of convolutional ANNs (CNNs). Using MATLAB, we evaluate CNN performance using systematically distorted ReLU functions, then substitute measured and simulated MMT transfer characteristics as proxies for ReLU. High classification accuracy is maintained, despite large variations in geometrical and electrical parameters, as CNNs use the same activation functions for training and classification.

This work studies a dynamic mechanism design problem in which a principal delegates decision makings to a group of privately-informed agents without the monetary transfer or burning. We consider that the principal privately possesses complete knowledge about the state transitions and study how she can use her private observation to support the incentive compatibility of the delegation via informational burning, a process we refer to as the looking-forward persuasion. The delegation mechanism is formulated in which the agents form belief hierarchies due to the persuasion and play a dynamic Bayesian game. We propose a novel randomized mechanism, known as Bayesian promised delegation (BPD), in which the periodic incentive compatibility is guaranteed by persuasions and promises of future delegations. We show that the BPD can achieve the same optimal social welfare as the original mechanism in stationary Markov perfect Bayesian equilibria. A revelation-principle-like design regime is established to show that the persuasion with belief hierarchies can be fully characterized by correlating the randomization of the agents' local BPD mechanisms with the persuasion as a direct recommendation of the future promises.

Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution. Many kinds of priors have been explored in the literature, from simple ones expressing local properties to more involved ones exploiting image redundancy at a non-local scale. In a departure from explicit modelling, several recent works have proposed and studied the use of implicit priors defined by an image denoising algorithm. This approach, commonly known as Plug & Play (PnP) regularisation, can deliver remarkably accurate results, particularly when combined with state-of-the-art denoisers based on convolutional neural networks. However, the theoretical analysis of PnP Bayesian models and algorithms is difficult and works on the topic often rely on unrealistic assumptions on the properties of the image denoiser. This papers studies maximum-a-posteriori (MAP) estimation for Bayesian models with PnP priors. We first consider questions related to existence, stability and well-posedness, and then present a convergence proof for MAP computation by PnP stochastic gradient descent (PnP-SGD) under realistic assumptions on the denoiser used. We report a range of imaging experiments demonstrating PnP-SGD as well as comparisons with other PnP schemes.