Efficient Monte Carlo for high excursions of Gaussian random fields

Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectations of functionals of the fields given the existence of excursions above high levels, b. Na\"{i}ve Monte Carlo takes an exponential, in b, computational cost to estimate these probabilities and conditional expectations for a prescribed relative accuracy. In contrast, our Monte Carlo procedures achieve, at worst, polynomial complexity in b, assuming only that the mean and covariance functions are H\"{o}lder continuous. We also explain how to fine tune the construction of our procedures in the presence of additional regularity, such as homogeneity and smoothness, in order to further improve the efficiency.Comment: Published in at http://dx.doi.org/10.1214/11-AAP792 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Practical Implementation of the Bernoulli Factory

The Bernoulli Factory is an algorithm that takes as input a series of i.i.d. Bernoulli random variables with an unknown but fixed success probability $p$, and outputs a corresponding series of Bernoulli random variables with success probability $f(p)$, where the function $f$ is known and defined on the interval $[0,1]$. While several practical uses of the method have been proposed in Monte Carlo applications, these require an implementation framework that is flexible, general and efficient. We present such a framework for functions that are either strictly linear, concave, or convex on the unit interval using a series of envelope functions defined through a cascade, and show that this method not only greatly reduces the number of input bits needed in practice compared to other currently proposed solutions for more specific problems, and is easy to specify for simple forms, but can easily be coupled to asymptotically efficient methods to allow for theoretically strong results.Comment: 23 page

Smoothed Variable Sample-size Accelerated Proximal Methods for Nonsmooth Stochastic Convex Programs

We consider minimizing $f(x) = \mathbb{E}[f(x,\omega)]$ when $f(x,\omega)$ is possibly nonsmooth and either strongly convex or convex in $x$. (I) Strongly convex. When $f(x,\omega)$ is $\mu-$strongly convex in $x$, we propose a variable sample-size accelerated proximal scheme (VS-APM) and apply it on $f_{\eta}(x)$, the ($\eta$-)Moreau smoothed variant of $\mathbb{E}[f(x,\omega)]$; we term such a scheme as (m-VS-APM). We consider three settings. (a) Bounded domains. In this setting, VS-APM displays linear convergence in inexact gradient steps, each of which requires utilizing an inner (SSG) scheme. Specifically, mVS-APM achieves an optimal oracle complexity in SSG steps; (b) Unbounded domains. In this regime, under a weaker assumption of suitable state-dependent bounds on subgradients, an unaccelerated variant mVS-PM is linearly convergent; (c) Smooth ill-conditioned $f$. When $f$ is $L$-smooth and $\kappa = L/\mu \ggg 1$, we employ mVS-APM where increasingly accurate gradients $\nabla_x f_{\eta}(x)$ are obtained by VS-APM. Notably, mVS-APM displays linear convergence and near-optimal complexity in inner proximal evaluations (upto a log factor) compared to VS-APM. But, unlike a direct application of VS-APM, this scheme is characterized by larger steplengths and better empirical behavior; (II) Convex. When $f(x,\omega)$ is merely convex but smoothable, by suitable choices of the smoothing, steplength, and batch-size sequences, smoothed VS-APM (or sVS-APM) produces sequences for which expected sub-optimality diminishes at the rate of $\mathcal{O}(1/k)$ with an optimal oracle complexity of $\mathcal{O}(1/\epsilon^2)$. Finally, sVS-APM and VS-APM produce sequences that converge almost surely to a solution of the original problem

Toxoplasma gondii-Induced Activation of EGFR Prevents Autophagy Protein-Mediated Killing of the Parasite

Toxoplasma gondii resides in an intracellular compartment (parasitophorous vacuole) that excludes transmembrane molecules required for endosome-lysosome recruitment. Thus, the parasite survives by avoiding lysosomal degradation. However, autophagy can re-route the parasitophorous vacuole to the lysosomes and cause parasite killing. This raises the possibility that T. gondii may deploy a strategy to prevent autophagic targeting to maintain the non-fusogenic nature of the vacuole. We report that T. gondii activated EGFR in endothelial cells, retinal pigment epithelial cells and microglia. Blockade of EGFR or its downstream molecule, Akt, caused targeting of the parasite by LC3(+) structures, vacuole-lysosomal fusion, lysosomal degradation and killing of the parasite that were dependent on the autophagy proteins Atg7 and Beclin 1. Disassembly of GPCR or inhibition of metalloproteinases did not prevent EGFR-Akt activation. T. gondii micronemal proteins (MICs) containing EGF domains (EGF-MICs; MIC3 and MIC6) appeared to promote EGFR activation. Parasites defective in EGF-MICs (MIC1 ko, deficient in MIC1 and secretion of MIC6; MIC3 ko, deficient in MIC3; and MIC1-3 ko, deficient in MIC1, MIC3 and secretion of MIC6) caused impaired EGFR-Akt activation and recombinant EGF-MICs (MIC3 and MIC6) caused EGFR-Akt activation. In cells treated with autophagy stimulators (CD154, rapamycin) EGFR signaling inhibited LC3 accumulation around the parasite. Moreover, increased LC3 accumulation and parasite killing were noted in CD154-activated cells infected with MIC1-3 ko parasites. Finally, recombinant MIC3 and MIC6 inhibited parasite killing triggered by CD154 particularly against MIC1-3 ko parasites. Thus, our findings identified EGFR activation as a strategy used by T. gondii to maintain the non-fusogenic nature of the parasitophorous vacuole and suggest that EGF-MICs have a novel role in affecting signaling in host cells to promote parasite survival

Trans-ancestry genome-wide association meta-analysis of prostate cancer identifies new susceptibility loci and informs genetic risk prediction.

Prostate cancer is a highly heritable disease with large disparities in incidence rates across ancestry populations. We conducted a multiancestry meta-analysis of prostate cancer genome-wide association studies (107,247 cases and 127,006 controls) and identified 86 new genetic risk variants independently associated with prostate cancer risk, bringing the total to 269 known risk variants. The top genetic risk score (GRS) decile was associated with odds ratios that ranged from 5.06 (95% confidence interval (CI), 4.84-5.29) for men of European ancestry to 3.74 (95% CI, 3.36-4.17) for men of African ancestry. Men of African ancestry were estimated to have a mean GRS that was 2.18-times higher (95% CI, 2.14-2.22), and men of East Asian ancestry 0.73-times lower (95% CI, 0.71-0.76), than men of European ancestry. These findings support the role of germline variation contributing to population differences in prostate cancer risk, with the GRS offering an approach for personalized risk prediction

AI is a viable alternative to high throughput screening: a 318-target study

: High throughput screening (HTS) is routinely used to identify bioactive small molecules. This requires physical compounds, which limits coverage of accessible chemical space. Computational approaches combined with vast on-demand chemical libraries can access far greater chemical space, provided that the predictive accuracy is sufficient to identify useful molecules. Through the largest and most diverse virtual HTS campaign reported to date, comprising 318 individual projects, we demonstrate that our AtomNet® convolutional neural network successfully finds novel hits across every major therapeutic area and protein class. We address historical limitations of computational screening by demonstrating success for target proteins without known binders, high-quality X-ray crystal structures, or manual cherry-picking of compounds. We show that the molecules selected by the AtomNet® model are novel drug-like scaffolds rather than minor modifications to known bioactive compounds. Our empirical results suggest that computational methods can substantially replace HTS as the first step of small-molecule drug discovery