Barrier Frank-Wolfe for Marginal Inference

We introduce a globally-convergent algorithm for optimizing the tree-reweighted (TRW) variational objective over the marginal polytope. The algorithm is based on the conditional gradient method (Frank-Wolfe) and moves pseudomarginals within the marginal polytope through repeated maximum a posteriori (MAP) calls. This modular structure enables us to leverage black-box MAP solvers (both exact and approximate) for variational inference, and obtains more accurate results than tree-reweighted algorithms that optimize over the local consistency relaxation. Theoretically, we bound the sub-optimality for the proposed algorithm despite the TRW objective having unbounded gradients at the boundary of the marginal polytope. Empirically, we demonstrate the increased quality of results found by tightening the relaxation over the marginal polytope as well as the spanning tree polytope on synthetic and real-world instances.Comment: 25 pages, 12 figures, To appear in Neural Information Processing Systems (NIPS) 2015, Corrected reference and cleaned up bibliograph

A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning

We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments---active user modelling with preferences, and hierarchical reinforcement learning---and a discussion of the pros and cons of Bayesian optimization based on our experiences

The OS* Algorithm: a Joint Approach to Exact Optimization and Sampling

Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is unrealistically slow in high-dimension spaces. The OS* algorithm that we propose is a unified approach to exact optimization and sampling, based on incremental refinements of a functional upper bound, which combines ideas of adaptive rejection sampling and of A* optimization search. We show that the choice of the refinement can be done in a way that ensures tractability in high-dimension spaces, and we present first experiments in two different settings: inference in high-order HMMs and in large discrete graphical models.Comment: 21 page

A Novel Framework for Online Amnesic Trajectory Compression in Resource-constrained Environments

State-of-the-art trajectory compression methods usually involve high space-time complexity or yield unsatisfactory compression rates, leading to rapid exhaustion of memory, computation, storage and energy resources. Their ability is commonly limited when operating in a resource-constrained environment especially when the data volume (even when compressed) far exceeds the storage limit. Hence we propose a novel online framework for error-bounded trajectory compression and ageing called the Amnesic Bounded Quadrant System (ABQS), whose core is the Bounded Quadrant System (BQS) algorithm family that includes a normal version (BQS), Fast version (FBQS), and a Progressive version (PBQS). ABQS intelligently manages a given storage and compresses the trajectories with different error tolerances subject to their ages. In the experiments, we conduct comprehensive evaluations for the BQS algorithm family and the ABQS framework. Using empirical GPS traces from flying foxes and cars, and synthetic data from simulation, we demonstrate the effectiveness of the standalone BQS algorithms in significantly reducing the time and space complexity of trajectory compression, while greatly improving the compression rates of the state-of-the-art algorithms (up to 45%). We also show that the operational time of the target resource-constrained hardware platform can be prolonged by up to 41%. We then verify that with ABQS, given data volumes that are far greater than storage space, ABQS is able to achieve 15 to 400 times smaller errors than the baselines. We also show that the algorithm is robust to extreme trajectory shapes.Comment: arXiv admin note: substantial text overlap with arXiv:1412.032

Sparse Identification and Estimation of Large-Scale Vector AutoRegressive Moving Averages

The Vector AutoRegressive Moving Average (VARMA) model is fundamental to the theory of multivariate time series; however, in practice, identifiability issues have led many authors to abandon VARMA modeling in favor of the simpler Vector AutoRegressive (VAR) model. Such a practice is unfortunate since even very simple VARMA models can have quite complicated VAR representations. We narrow this gap with a new optimization-based approach to VARMA identification that is built upon the principle of parsimony. Among all equivalent data-generating models, we seek the parameterization that is "simplest" in a certain sense. A user-specified strongly convex penalty is used to measure model simplicity, and that same penalty is then used to define an estimator that can be efficiently computed. We show that our estimator converges to a parsimonious element in the set of all equivalent data-generating models, in a double asymptotic regime where the number of component time series is allowed to grow with sample size. Further, we derive non-asymptotic upper bounds on the estimation error of our method relative to our specially identified target. Novel theoretical machinery includes non-asymptotic analysis of infinite-order VAR, elastic net estimation under a singular covariance structure of regressors, and new concentration inequalities for quadratic forms of random variables from Gaussian time series. We illustrate the competitive performance of our methods in simulation and several application domains, including macro-economic forecasting, demand forecasting, and volatility forecasting

Forecasting and policy making

This chapter investigates the use of economic forecasting in policy making. Forecasts are used in many policy areas to project the consequences of particular policy measures for policymakers’ targets. After reviewing some important forecasts of fiscal authorities and central banks, we proceed to focus on the role of forecasts in monetary policy. A formal framework serves to differentiate the role of forecasts in simple feedback rules versus optimal control policies. We then provide empirical evidence that central bank policies in the United States and the euro area are well described by interest rate rules responding to forecasts of inflation and economic activity rather than outcomes. Next, we provide a detailed exposition of methods for producing forecasts and the associated forecasting models. Practical applications with U.S. or euro area data are reported. Particular issues discussed include the use of economic structure in interpreting forecasts and the implementation of different conditioning assumptions regarding future policy that play a role in practice. We also compare the accuracy of model and expert forecasts and measure the degree of forecast heterogeneity. Finally, we utilize macroeconomic models to study the interaction of forecasting and policy by evaluating the performance and robustness of forecast versu

Action and behavior: a free-energy formulation

We have previously tried to explain perceptual inference and learning under a free-energy principle that pursues Helmholtz’s agenda to understand the brain in terms of energy minimization. It is fairly easy to show that making inferences about the causes of sensory data can be cast as the minimization of a free-energy bound on the likelihood of sensory inputs, given an internal model of how they were caused. In this article, we consider what would happen if the data themselves were sampled to minimize this bound. It transpires that the ensuing active sampling or inference is mandated by ergodic arguments based on the very existence of adaptive agents. Furthermore, it accounts for many aspects of motor behavior; from retinal stabilization to goal-seeking. In particular, it suggests that motor control can be understood as fulfilling prior expectations about proprioceptive sensations. This formulation can explain why adaptive behavior emerges in biological agents and suggests a simple alternative to optimal control theory. We illustrate these points using simulations of oculomotor control and then apply to same principles to cued and goal-directed movements. In short, the free-energy formulation may provide an alternative perspective on the motor control that places it in an intimate relationship with perception