Variational Bayes With Intractable Likelihood

Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes their use in many interesting situations such as in state--space models and in approximate Bayesian computation (ABC), where application of VB methods was previously impossible. This article extends the scope of application of VB to cases where the likelihood is intractable, but can be estimated unbiasedly. The proposed VB method therefore makes it possible to carry out Bayesian inference in many statistical applications, including state--space models and ABC. The method is generic in the sense that it can be applied to almost all statistical models without requiring too much model-based derivation, which is a drawback of many existing VB algorithms. We also show how the proposed method can be used to obtain highly accurate VB approximations of marginal posterior distributions. Supplementary material for this article is available online.     

Low rank matrix recovery from rank one measurements

We study the recovery of Hermitian low rank matrices $X\in {\mathbb{C}}^{n\times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form $a_j{a}_j^{?}$ for some measurement vectors $a_1,\dots ,a_m$, i.e., the measurements are given by $b_j=\mathrm{tr}(X{a}_j{a}_j^{?})$. The case where the matrix $X=x{x}^{?}$ to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements $b_j=|〈x,a_j〉{|}^2$) via the PhaseLift approach, which has been introduced recently. We derive bounds for the number m of measurements that guarantee successful uniform recovery of Hermitian rank r matrices, either for the vectors $a_j$, $j=1,\dots ,m$, being chosen independently at random according to a standard Gaussian distribution, or $a_j$ being sampled independently from an (approximate) complex projective t-design with $t=4$. In the Gaussian case, we require $m\ge Crn$ measurements, while in the case of 4-designs we need $m\ge \mathit{Cr}n\log ?(n)$. Our results are uniform in the sense that one random choice of the measurement vectors $a_j$ guarantees recovery of all rank r-matrices simultaneously with high probability. Moreover, we prove robustness of recovery under perturbation of the measurements by noise. The result for approximate 4-designs generalizes and improves a recent bound on phase retrieval due to Gross, Krahmer and Kueng. In addition, it has applications in quantum state tomography. Our proofs employ the so-called bowling scheme which is based on recent ideas by Mendelson and Koltchinskii.     

Tensor Decomposition With Generalized Lasso Penalties

We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multiway data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner parallel to the generalized lasso for regression and smoothing problems. Our approach presents many nontrivial challenges at the intersection of modeling and computation, which are studied in detail. An efficient coordinate-wise optimization algorithm for PTD is presented, and its convergence properties are characterized. The method is applied both to simulated data and real data on flu hospitalizations in Texas and motion-capture data from video cameras. These results show that our penalized tensor decomposition can offer major improvements on existing methods for analyzing multiway data that exhibit smooth spatial or temporal features.     

Quadratic cone cutting surfaces for quadratic programs with on–off constraints

We study the convex hull of a set arising as a relaxation of difficult convex mixed integer quadratic programs (MIQP). We characterize the extreme points of the convex hull of the set and the extreme points of its continuous relaxation. We derive four quadratic cutting surfaces that improve the strength of the continuous relaxation. Each of the cutting surfaces is second-order-cone representable. Via a shooting experiment, we provide empirical evidence as to the importance of each inequality type in improving the relaxation. Computational results that employ the new cutting surfaces to strengthen the relaxation for MIQPs arising from portfolio optimization applications are promising.     

A complete characterization of disjunctive conic cuts for mixed integer second order cone optimization

We study the convex hull of the intersection of a disjunctive set defined by parallel hyperplanes and the feasible set of a mixed integer second order cone optimization (MISOCO) problem. We extend our prior work on disjunctive conic cuts (DCCs), which has thus far been restricted to the case in which the intersection of the hyperplanes and the feasible set is bounded. Using a similar technique, we show that one can extend our previous results to the case in which that intersection is unbounded. We provide a complete characterization in closed form of the conic inequalities required to describe the convex hull when the hyperplanes defining the disjunction are parallel.     

Comparative Studies of Selected Criteria Enabling Optimization of the Extraction of Polar Biologically Active Compounds from Alfalfa with Supercritical Carbon Dioxide

The aim of this research was to provide crucial and useful data about the selection of the optimization criteria of supercritical carbon dioxide extraction of alfalfa at a quarter-technical plant. The correlation between more general output, including total phenolics and flavonoids content, and a more specified composition of polar constituents was extensively studied. In all alfalfa extracts, polar bioactive constituents were analyzed by both spectrometric (general output) and chromatographic (detailed output) analyses. Eight specific phenolic acids and nine flavonoids were determined. The most dominant were salicylic acid (221.41 µg g⁻¹), ferulic acid (119.73 µg g⁻¹), quercetin (2.23 µg g⁻¹), and apigenin (2.60 µg g⁻¹). For all seventeen analyzed compounds, response surface methodology and analysis of variance were used to provide the optimal conditions of supercritical fluid extraction for each individual constituent. The obtained data have shown that eight of those compounds have a similar range of optimal process parameters, being significantly analogous for optimization based on total flavonoid content.     

Optimization of Vacuum-Microwave-Assisted Extraction of Natural Polyphenols and Flavonoids from Raw Solid Waste of the Orange Juice Producing Industry at Industrial Scale

Orange pomace (OP) is a solid waste produced in bulk as a byproduct of the orange juice industry and accounts for approximately 50% of the quantity of the fruits processed into juice. In numerous literature references there is information about diverse uses of orange pomace for the production of high-added-value products including production of natural antioxidant and antimicrobial extracts rich in polyphenols and flavonoids which can substitute the hazardous chemical antioxidants/antimicrobials used in agro-food and cosmetics sectors. In this work and for the first time, according to our knowledge, the eco-friendly aqueous vacuum microwave assisted extraction of orange pomace was investigated and optimized at real industrial scale in order to produce aqueous antioxidant/antimicrobial extracts. A Response Surface Optimization methodology with a multipoint historical data experimental design was employed to obtain the optimal values of the process parameters in order to achieve the maximum rates of extraction of OP total polyphenols and/or total flavonoids for economically optimum production at industrial scale. The three factors used for the optimization were: (a) microwave power (b) water to raw pomace ratio and (c) extraction time. Moreover, the effectiveness and statistical soundness of the derived cubic polynomial predictive models were verified by ANOVA.     

Impact of Collection Volume and DNA Extraction Method on the Detection of Biomarkers and HPV DNA in First-Void Urine

The potential of first-void (FV) urine as a non-invasive liquid biopsy for detection of human papillomavirus (HPV) DNA and other biomarkers has been increasingly recognized over the past decade. In this study, we investigated whether the volume of this initial urine stream has an impact on the analytical performance of biomarkers. In parallel, we evaluated different DNA extraction protocols and introduced an internal control in the urine preservative. Twenty-five women, diagnosed with high-risk HPV, provided three home-collected FV urine samples using three FV urine collection devices (Colli-Pee) with collector tubes that differ in volume (4, 10, 20 mL). Each collector tube was prefilled with Urine Conservation Medium spiked with phocine herpesvirus 1 (PhHV-1) DNA as internal control. Five different DNA extraction protocols were compared, followed by PCR for GAPDH and PhHV-1 (qPCR), HPV DNA, and HBB (HPV-Risk Assay), and ACTB (methylation-specific qPCR). Results showed limited effects of collection volume on human and HPV DNA endpoints. In contrast, significant variations in yield for human endpoints were observed for different DNA extraction methods (p < 0.05). Additionally, the potential of PhHV-1 as internal control to monitor FV urine collection, storage, and processing was demonstrated.     

Evaluation of Multi-Objective Optimization Algorithms for NMR Chemical Shift Assignment

An automated NMR chemical shift assignment algorithm was developed using multi-objective optimization techniques. The problem is modeled as a combinatorial optimization problem and its objective parameters are defined separately in different score functions. Some of the heuristic approaches of evolutionary optimization are employed in this problem model. Both, a conventional genetic algorithm and multi-objective methods, i.e., the non-dominated sorting genetic algorithms II and III (NSGA2 and NSGA3), are applied to the problem. The multi-objective approaches consider each objective parameter separately, whereas the genetic algorithm followed a conventional way, where all objectives are combined in one score function. Several improvement steps and repetitions on these algorithms are performed and their combinations are also created as a hyper-heuristic approach to the problem. Additionally, a hill-climbing algorithm is also applied after the evolutionary algorithm steps. The algorithms are tested on several different datasets with a set of 11 commonly used spectra. The test results showed that our algorithm could assign both sidechain and backbone atoms fully automatically without any manual interactions. Our approaches could provide around a 65% success rate and could assign some of the atoms that could not be assigned by other methods.