The Limitations of Optimization from Samples

In this paper we consider the following question: can we optimize objective functions from the training data we use to learn them? We formalize this question through a novel framework we call optimization from samples (OPS). In OPS, we are given sampled values of a function drawn from some distribution and the objective is to optimize the function under some constraint. While there are interesting classes of functions that can be optimized from samples, our main result is an impossibility. We show that there are classes of functions which are statistically learnable and optimizable, but for which no reasonable approximation for optimization from samples is achievable. In particular, our main result shows that there is no constant factor approximation for maximizing coverage functions under a cardinality constraint using polynomially-many samples drawn from any distribution. We also show tight approximation guarantees for maximization under a cardinality constraint of several interesting classes of functions including unit-demand, additive, and general monotone submodular functions, as well as a constant factor approximation for monotone submodular functions with bounded curvature

Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis-Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler's exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the \emph{exact} posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this paper: when the likelihood has some \emph{local} regularity, the number of model evaluations per MCMC step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ODE and PDE inference problems, with both synthetic and real data.Comment: A major update of the theory and example

Development and optimization of a miniaturized western blot-based screening platform to identify regulators of post-translational modifications

Post-translational modifications (PTMs) are fundamental traits of protein functionality and their study has been addressed using several approaches over the past years. However, screening methods developed to detect regulators of PTMs imply many challenges and are usually based on expensive techniques. Herein, we described the development and optimization of a western blot-based platform for identification of regulators of a specific PTM—mono-ubiquitylation of proliferating cell nuclear antigen (PCNA). This cell-based method does not require specific equipment, apart from the basic western blot (WB) devices and minor accessories, which are accessible for most research labs. The modifications introduced to the classical WB protocol allow the performance of PTM analysis from a single well of a 96-well plate with minimal sample manipulation and low intra- and inter-plate variability, making this method ideal to screen arrayed compound libraries in a 96-well format. As such, our experimental pipeline provides the proof of concept to design small screenings of PTM regulators by improving the quantitative accuracy and throughput capacity of classical western blots.Fil: Villafañez, Florencia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigaciones en Bioquímica Clínica e Inmunología; Argentina. Universidad Nacional de Córdoba; ArgentinaFil: Gottifredi, Vanesa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquímicas de Buenos Aires. Fundación Instituto Leloir. Instituto de Investigaciones Bioquímicas de Buenos Aires; ArgentinaFil: Soria, Ramiro Gaston. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigaciones en Bioquímica Clínica e Inmunología; Argentin