Neural Dynamics of Autistic Behaviors: Cognitive, Emotional, and Timing Substrates

What brain mechanisms underlie autism and how do they give rise to autistic behavioral symptoms? This article describes a neural model, called the iSTART model, which proposes how cognitive, emotional, timing, and motor processes may interact together to create and perpetuate autistic symptoms. These model processes were originally developed to explain data concerning how the brain controls normal behaviors. The iSTART model shows how autistic behavioral symptoms may arise from prescribed breakdowns in these brain processes.Air Force Office of Scientific Research (F49620-01-1-0397); Office of Naval Research (N00014-01-1-0624

Hamiltonian Monte Carlo Acceleration Using Surrogate Functions with Random Bases

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov Chain Monte Carlo (MCMC) methods, namely, Hamiltonian Monte Carlo (HMC). The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the art methods

Unbiased and Consistent Nested Sampling via Sequential Monte Carlo

We introduce a new class of sequential Monte Carlo methods called Nested Sampling via Sequential Monte Carlo (NS-SMC), which reframes the Nested Sampling method of Skilling (2006) in terms of sequential Monte Carlo techniques. This new framework allows convergence results to be obtained in the setting when Markov chain Monte Carlo (MCMC) is used to produce new samples. An additional benefit is that marginal likelihood estimates are unbiased. In contrast to NS, the analysis of NS-SMC does not require the (unrealistic) assumption that the simulated samples be independent. As the original NS algorithm is a special case of NS-SMC, this provides insights as to why NS seems to produce accurate estimates despite a typical violation of its assumptions. For applications of NS-SMC, we give advice on tuning MCMC kernels in an automated manner via a preliminary pilot run, and present a new method for appropriately choosing the number of MCMC repeats at each iteration. Finally, a numerical study is conducted where the performance of NS-SMC and temperature-annealed SMC is compared on several challenging and realistic problems. MATLAB code for our experiments is made available at https://github.com/LeahPrice/SMC-NS .Comment: 45 pages, some minor typographical errors fixed since last versio

The Limits of Post-Selection Generalization

While statistics and machine learning offers numerous methods for ensuring generalization, these methods often fail in the presence of adaptivity---the common practice in which the choice of analysis depends on previous interactions with the same dataset. A recent line of work has introduced powerful, general purpose algorithms that ensure post hoc generalization (also called robust or post-selection generalization), which says that, given the output of the algorithm, it is hard to find any statistic for which the data differs significantly from the population it came from. In this work we show several limitations on the power of algorithms satisfying post hoc generalization. First, we show a tight lower bound on the error of any algorithm that satisfies post hoc generalization and answers adaptively chosen statistical queries, showing a strong barrier to progress in post selection data analysis. Second, we show that post hoc generalization is not closed under composition, despite many examples of such algorithms exhibiting strong composition properties