Bayesian approaches developed to solve the optimal design of sequential experiments are mathematically elegant but computationally challenging. Recently, techniques using amortization have been proposed to make these Bayesian approaches practical, by training a parameterized policy that proposes designs efficiently at deployment time. However, these methods may not sufficiently explore the design space, require access to a differentiable probabilistic model and can only optimize over continuous design spaces. Here, we address these limitations by showing that the problem of optimizing policies can be reduced to solving a Markov decision process (MDP). We solve the equivalent MDP with modern deep reinforcement learning techniques. Our experiments show that our approach is also computationally efficient at deployment time and exhibits state-of-the-art performance on both continuous and discrete design spaces, even when the probabilistic model is a black box.

Simulation models, in particular agent-based models, are gaining popularity in economics. The considerable flexibility they offer, as well as their capacity to reproduce a variety of empirically observed behaviours of complex systems, give them broad appeal, and the increasing availability of cheap computing power has made their use feasible. Yet a widespread adoption in real-world modelling and decision-making scenarios has been hindered by the difficulty of performing parameter estimation for such models. In general, simulation models lack a tractable likelihood function, which precludes a straightforward application of standard statistical inference techniques. Several recent works have sought to address this problem through the application of likelihood-free inference techniques, in which parameter estimates are determined by performing some form of comparison between the observed data and simulation output. However, these approaches are (a) founded on restrictive assumptions, and/or (b) typically require many hundreds of thousands of simulations. These qualities make them unsuitable for large-scale simulations in economics and can cast doubt on the validity of these inference methods in such scenarios. In this paper, we investigate the efficacy of two classes of black-box approximate Bayesian inference methods that have recently drawn significant attention within the probabilistic machine learning community: neural posterior estimation and neural density ratio estimation. We present benchmarking experiments in which we demonstrate that neural network based black-box methods provide state of the art parameter inference for economic simulation models, and crucially are compatible with generic multivariate time-series data. In addition, we suggest appropriate assessment criteria for future benchmarking of approximate Bayesian inference procedures for economic simulation models.

Until now, neural networks have been predominantly relying on backpropagation and gradient descent as the inference engine in order to learn a neural network's parameters. This is primarily because closed-form Bayesian inference for neural networks has been considered to be intractable. This short paper outlines a new analytical method for performing tractable approximate Gaussian inference (TAGI) in Bayesian neural networks.

The characterization of an exoplanet's interior is an inverse problem, which requires statistical methods such as Bayesian inference in order to be solved. Current methods employ Markov Chain Monte Carlo (MCMC) sampling to infer the posterior probability of planetary structure parameters for a given exoplanet. These methods are time consuming since they require the calculation of a large number of planetary structure models. To speed up the inference process when characterizing an exoplanet, we propose to use conditional invertible neural networks (cINNs) to calculate the posterior probability of the internal structure parameters. cINNs are a special type of neural network which excel in solving inverse problems. We constructed a cINN using FrEIA, which was then trained on a database of $5.6\cdot 10^6$ internal structure models to recover the inverse mapping between internal structure parameters and observable features (i.e., planetary mass, planetary radius and composition of the host star). The cINN method was compared to a Metropolis-Hastings MCMC. For that we repeated the characterization of the exoplanet K2-111 b, using both the MCMC method and the trained cINN. We show that the inferred posterior probability of the internal structure parameters from both methods are very similar, with the biggest differences seen in the exoplanet's water content. Thus cINNs are a possible alternative to the standard time-consuming sampling methods. Indeed, using cINNs allows for orders of magnitude faster inference of an exoplanet's composition than what is possible using an MCMC method, however, it still requires the computation of a large database of internal structures to train the cINN. Since this database is only computed once, we found that using a cINN is more efficient than an MCMC, when more than 10 exoplanets are characterized using the same cINN.

This paper provides a unified perspective for the Kullback-Leibler (KL)-divergence and the integral probability metrics (IPMs) from the perspective of maximum likelihood density-ratio estimation (DRE). Both the KL-divergence and the IPMs are widely used in various fields in applications such as generative modeling. However, a unified understanding of these concepts has still been unexplored. In this paper, we show that the KL-divergence and the IPMs can be represented as maximal likelihoods differing only by sampling schemes, and use this result to derive a unified form of the IPMs and a relaxed estimation method. To develop the estimation problem, we construct an unconstrained maximum likelihood estimator to perform DRE with a stratified sampling scheme. We further propose a novel class of probability divergences, called the Density Ratio Metrics (DRMs), that interpolates the KL-divergence and the IPMs. In addition to these findings, we also introduce some applications of the DRMs, such as DRE and generative adversarial networks. In experiments, we validate the effectiveness of our proposed methods.

Probability for improved business decisions: Introduction, Combinatorics, Bayesian Inference, Distributions. Welcome to Probability and Statistics for Business and Data Science! In this course we cover what you need to know about probability and statistics to succeed in business and the data science field! This practical course will go over theory and implementation of statistics to real world problems. Each section has example problems, in course quizzes, and assessment tests.

This paper addresses the problem of precisely estimating the parameters of a stochastic model corresponding to branching processes. A branching process is a stochastic process consisting of collections of random variables indexed by the natural numbers. Branching processes are often used to describe population models Jagers (1989) and Athreya and Ney (2012); for example, models in the population genetics showing the genetic drift Burden and Simon (2016) Chen et al. (2017). In contrast to statistical approaches, branching processes enable the study of the dynamics of cell evolution and, as a consistence, have become a popular approach to cancer cell evolution research West et al., 2016. However, particularly in the case of cancer cell evolution, as well as in branching processes in general, the ultimate extinction of a population often occurs Devroye (1998). It is for this reason that with the initial uniform distribution of parameters, branching processes models tend to yield unevenly distributed data consisting of sparse and dense regions. The stochastic nature of the data is an another obstacle in estimating the parameters of a branching processes model, especially in the case of cancer cell evolution Nagornov et al. (2021). Moreover, simulations, based on a model of cell mutations, population evolution, and tumor/cancer subpopulations, commonly lead to the emergence of many clones and rarely to the appearance of cancer cells.

Generative Adversarial Networks (GANs) software is software for producing forgeries and imitations of data (aka synthetic data, fake data). Human beings have been making fakes, with good or evil intent, of almost everything they possibly can, since the beginning of the human race. Thus, perhaps not too surprisingly, GAN software has been widely used since it was first proposed in this amazingly recent 2014 paper. To gauge how widely GAN software has been used so far, see, for example, this 2019 article entitled "18 Impressive Applications of Generative Adversarial Networks (GANs)" Sounds (voices, music,…), Images (realistic pictures, paintings, drawings, handwriting, …), Text,etc. The forgeries can be tweaked so that they range from being very similar to the originals, to being whimsical exaggerations thereof.

Applications of neural networks have achieved great success in various fields. A major extension of the standard neural networks is to make them stochastic, namely, to make the output a random function of the input. In a broad sense, stochastic neural networks include neural networks trained with dropout (Srivastava et al., 2014; Gal & Ghahramani, 2016), Bayesian networks (Mackay, 1992), variational autoencoders (VAE) (Kingma & Welling, 2013), and generative adversarial networks (Goodfellow et al., 2014). There are many reasons why one wants to make a neural network stochastic. Two main reasons are (1) regularization and (2) distribution modeling.

Random partition models are widely used in Bayesian methods for various clustering tasks, such as mixture models, topic models, and community detection problems. While the number of clusters induced by random partition models has been studied extensively, another important model property regarding the balancedness of cluster sizes has been largely neglected. We formulate a framework to define and theoretically study the balancedness of exchangeable random partition models, by analyzing how a model assigns probabilities to partitions with different levels of balancedness. We demonstrate that the "rich-get-richer" characteristic of many existing popular random partition models is an inevitable consequence of two common assumptions: product-form exchangeability and projectivity. We propose a principled way to compare the balancedness of random partition models, which gives a better understanding of what model works better and what doesn't for different applications. We also introduce the "rich-get-poorer" random partition models and illustrate their application to entity resolution tasks.