Bayesian Deep Net GLM and GLMM

Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The consideration of neural networks with random effects is not widely used in the literature, perhaps because of the computational challenges of incorporating subject specific parameters into already complex models. Efficient computational methods for high-dimensional Bayesian inference are developed using Gaussian variational approximation, with a parsimonious but flexible factor parametrization of the covariance matrix. We implement natural gradient methods for the optimization, exploiting the factor structure of the variational covariance matrix in computation of the natural gradient. Our flexible DFNN models and Bayesian inference approach lead to a regression and classification method that has a high prediction accuracy, and is able to quantify the prediction uncertainty in a principled and convenient way. We also describe how to perform variable selection in our deep learning method. The proposed methods are illustrated in a wide range of simulated and real-data examples, and the results compare favourably to a state of the art flexible regression and classification method in the statistical literature, the Bayesian additive regression trees (BART) method. User-friendly software packages in Matlab, R and Python implementing the proposed methods are available at https://github.com/VBayesLabComment: 35 pages, 7 figure, 10 table

A Semi-parametric Analysis of Technology, with an Application to U.S. Dairy Farms

This article proposes a semi-parametric stochastic frontier model (SPSF) in which components of the technology and of technical efficiency are represented using semi-parametric methods and estimated in a Bayesian framework. The approach is illustrated in an application to US farm data. The analysis shows important scale economies for small and medium herds and constant return to scale for larger herds. With the exception of labor, estimates of marginal products were close to the value expected under profit maximization. Finally, the results suggest important opportunities to increase productivity through reductions in technical inefficiencies.

Analyzing Differences in Rural Hospital Efficiency: A Data Envelopment Analysis Approach

This study analyzes difference in efficiency among the U.S. rural hospitals using a two-stage, semi-parametric approach. Data Envelopment Analysis is used in the first stage to calculate cost, technical and allocative efficiencies of Critical Access Hospitals (CAH) and non-CAH rural hospitals. Following Simar and Wilson (2007), bootstrapped truncated regressions are used in the second stage to infer on relationship between the cost, technical and allocative inefficiencies of hospitals and some environmental variables. The estimated results show that CAHs are less cost, technical and allocative efficient than non-CAH rural hospitals. The results also show that Medicare cost-based reimbursement for CAHs has a negative effect on the efficiency of these hospitals while Medicare prospective payment system for non-CAH rural hospitals has a positive effect on hospital efficiency.efficiency, two-stage, semi-parametric, bootstrap, data envelopment analysis, Health Economics and Policy, I12, I18,

Bayesian Optimization for Probabilistic Programs

We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any graphical model, can be optimized with respect to an arbitrary subset of its sampled variables. To carry out this optimization, we develop the first Bayesian optimization package to directly exploit the source code of its target, leading to innovations in problem-independent hyperpriors, unbounded optimization, and implicit constraint satisfaction; delivering significant performance improvements over prominent existing packages. We present applications of our method to a number of tasks including engineering design and parameter optimization

Capacity Constrained Influence Maximization in Social Networks

Influence maximization (IM) aims to identify a small number of influential individuals to maximize the information spread and finds applications in various fields. It was first introduced in the context of viral marketing, where a company pays a few influencers to promote the product. However, apart from the cost factor, the capacity of individuals to consume content poses challenges for implementing IM in real-world scenarios. For example, players on online gaming platforms can only interact with a limited number of friends. In addition, we observe that in these scenarios, (i) the initial adopters of promotion are likely to be the friends of influencers rather than the influencers themselves, and (ii) existing IM solutions produce sub-par results with high computational demands. Motivated by these observations, we propose a new IM variant called capacity constrained influence maximization (CIM), which aims to select a limited number of influential friends for each initial adopter such that the promotion can reach more users. To solve CIM effectively, we design two greedy algorithms, MG-Greedy and RR-Greedy, ensuring the $1/2$-approximation ratio. To improve the efficiency, we devise the scalable implementation named RR-OPIM+ with $(1/2-\epsilon)$-approximation and near-linear running time. We extensively evaluate the performance of 9 approaches on 6 real-world networks, and our solutions outperform all competitors in terms of result quality and running time. Additionally, we deploy RR-OPIM+ to online game scenarios, which improves the baseline considerably.Comment: The technical report of the paper entitled 'Capacity Constrained Influence Maximization in Social Networks' in SIGKDD'2

How should be the levels of public and private R&D investments to trigger modern productivity growth? Empirical evidence and lessons learned for Italian economy

Governments in modern economies devote much policy attention to enhancing productivity and continue to emphasize its drivers such as investment in R&D. This paper analyzes the relationship between productivity growth and levels of public and private R&D expenditures. The economic analysis shows that the magnitude of R&D expenditure by business enterprise equal to 1.58% (% of GDP) and R&D expenditure of government and higher education of 1.06 (% of GDP) maximize the long-run impact on productivity growth. These optimal rates are the key to sustain productivity and technology improvements that are more and more necessary to modern economic growth.R&D investment, Productivity growth, Optimization

Measurement of Returns-to-Scale using Interval Data Envelopment Analysis Models

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI linkThe economic concept of Returns-to-Scale (RTS) has been intensively studied in the context of Data Envelopment Analysis (DEA). The conventional DEA models that are used for RTS classification require well-defined and accurate data whereas in reality observations gathered from production systems may be characterized by intervals. For instance, the heat losses of the combined production of heat and power (CHP) systems may be within a certain range, hinging on a wide variety of factors such as external temperature and real-time energy demand. Enriching the current literature independently tackling the two problems; interval data and RTS estimation; we develop an overarching evaluation process for estimating RTS of Decision Making Units (DMUs) in Imprecise DEA (IDEA) where the input and output data lie within bounded intervals. In the presence of interval data, we introduce six types of RTS involving increasing, decreasing, constant, non-increasing, non-decreasing and variable RTS. The situation for non-increasing (non-decreasing) RTS is then divided into two partitions; constant or decreasing (constant or increasing) RTS using sensitivity analysis. Additionally, the situation for variable RTS is split into three partitions consisting of constant, decreasing and increasing RTS using sensitivity analysis. Besides, we present the stability region of an observation while preserving its current RTS classification using the optimal values of a set of proposed DEA-based models. The applicability and efficacy of the developed approach is finally studied through two numerical examples and a case study

Dual RL: Unification and New Methods for Reinforcement and Imitation Learning

The goal of reinforcement learning (RL) is to maximize the expected cumulative return. It has been shown that this objective can be represented by an optimization problem of the state-action visitation distribution under linear constraints. The dual problem of this formulation, which we refer to as dual RL, is unconstrained and easier to optimize. We show that several state-of-the-art off-policy deep reinforcement learning (RL) algorithms, under both online and offline, RL and imitation learning (IL) settings, can be viewed as dual RL approaches in a unified framework. This unification provides a common ground to study and identify the components that contribute to the success of these methods and also reveals the common shortcomings across methods with new insights for improvement. Our analysis shows that prior off-policy imitation learning methods are based on an unrealistic coverage assumption and are minimizing a particular f-divergence between the visitation distributions of the learned policy and the expert policy. We propose a new method using a simple modification to the dual RL framework that allows for performant imitation learning with arbitrary off-policy data to obtain near-expert performance, without learning a discriminator. Further, by framing a recent SOTA offline RL method XQL in the dual RL framework, we propose alternative choices to replace the Gumbel regression loss, which achieve improved performance and resolve the training instability issue of XQL. Project code and details can be found at this https://hari-sikchi.github.io/dual-rl.Comment: 46 pages. Under revie