A Bayesian approach to constrained single- and multi-objective optimization

This article addresses the problem of derivative-free (single- or multi-objective) optimization subject to multiple inequality constraints. Both the objective and constraint functions are assumed to be smooth, non-linear and expensive to evaluate. As a consequence, the number of evaluations that can be used to carry out the optimization is very limited, as in complex industrial design optimization problems. The method we propose to overcome this difficulty has its roots in both the Bayesian and the multi-objective optimization literatures. More specifically, an extended domination rule is used to handle objectives and constraints in a unified way, and a corresponding expected hyper-volume improvement sampling criterion is proposed. This new criterion is naturally adapted to the search of a feasible point when none is available, and reduces to existing Bayesian sampling criteria---the classical Expected Improvement (EI) criterion and some of its constrained/multi-objective extensions---as soon as at least one feasible point is available. The calculation and optimization of the criterion are performed using Sequential Monte Carlo techniques. In particular, an algorithm similar to the subset simulation method, which is well known in the field of structural reliability, is used to estimate the criterion. The method, which we call BMOO (for Bayesian Multi-Objective Optimization), is compared to state-of-the-art algorithms for single- and multi-objective constrained optimization

Testing Conditional Independence of Discrete Distributions

We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with probability at least $2/3$, between the case that $X$ and $Y$ are conditionally independent given $Z$ from the case that $(X, Y, Z)$ is $\epsilon$-far, in $\ell_1$-distance, from every distribution that has this property. Conditional independence is a concept of central importance in probability and statistics with a range of applications in various scientific domains. As such, the statistical task of testing conditional independence has been extensively studied in various forms within the statistics and econometrics communities for nearly a century. Perhaps surprisingly, this problem has not been previously considered in the framework of distribution property testing and in particular no tester with sublinear sample complexity is known, even for the important special case that the domains of $X$ and $Y$ are binary. The main algorithmic result of this work is the first conditional independence tester with {\em sublinear} sample complexity for discrete distributions over $[\ell_1]\times[\ell_2] \times [n]$. To complement our upper bounds, we prove information-theoretic lower bounds establishing that the sample complexity of our algorithm is optimal, up to constant factors, for a number of settings. Specifically, for the prototypical setting when $\ell_1, \ell_2 = O(1)$, we show that the sample complexity of testing conditional independence (upper bound and matching lower bound) is \[ \Theta\left({\max\left(n^{1/2}/\epsilon^2,\min\left(n^{7/8}/\epsilon,n^{6/7}/\epsilon^{8/7}\right)\right)}\right)\,. \

Present and Future CP Measurements

We review theoretical and experimental results on CP violation summarizing the discussions in the working group on CP violation at the UK phenomenology workshop 2000 in Durham.Comment: 104 pages, Latex, to appear in Journal of Physics

Urinary MicroRNA Profiling in the Nephropathy of Type 1 Diabetes

Background: Patients with Type 1 Diabetes (T1D) are particularly vulnerable to development of Diabetic nephropathy (DN) leading to End Stage Renal Disease. Hence a better understanding of the factors affecting kidney disease progression in T1D is urgently needed. In recent years microRNAs have emerged as important post-transcriptional regulators of gene expression in many different health conditions. We hypothesized that urinary microRNA profile of patients will differ in the different stages of diabetic renal disease. Methods and Findings: We studied urine microRNA profiles with qPCR in 40 T1D with >20 year follow up 10 who never developed renal disease (N) matched against 10 patients who went on to develop overt nephropathy (DN), 10 patients with intermittent microalbuminuria (IMA) matched against 10 patients with persistent (PMA) microalbuminuria. A Bayesian procedure was used to normalize and convert raw signals to expression ratios. We applied formal statistical techniques to translate fold changes to profiles of microRNA targets which were then used to make inferences about biological pathways in the Gene Ontology and REACTOME structured vocabularies. A total of 27 microRNAs were found to be present at significantly different levels in different stages of untreated nephropathy. These microRNAs mapped to overlapping pathways pertaining to growth factor signaling and renal fibrosis known to be targeted in diabetic kidney disease. Conclusions: Urinary microRNA profiles differ across the different stages of diabetic nephropathy. Previous work using experimental, clinical chemistry or biopsy samples has demonstrated differential expression of many of these microRNAs in a variety of chronic renal conditions and diabetes. Combining expression ratios of microRNAs with formal inferences about their predicted mRNA targets and associated biological pathways may yield useful markers for early diagnosis and risk stratification of DN in T1D by inferring the alteration of renal molecular processes. © 2013 Argyropoulos et al

A First-Order Representation for Knowledge Discovery

In this paper we consider different representations for relational learning problems, with the aim of making ILP methods more applicable to real-world problems. In the past, ILP tended to concentrate on the term representation, with the flattened Datalog representation as a `poor man's version'. There has been relatively little emphasis on database-oriented representations, using e.g. the relational datamodel or the Entity-Relationship model. On the other hand, much of the available data is stored in multi-relational databases. Even if we don't actually interface our ILP systems with a DBMS, we need to understand the database representation sufficiently in order to convert it to an ILP representation. Such conversions and relations between different representations are the subject of this paper. We consider four different representations: the Entity-Relationship model, the relational model, a flattened individual-centred representation based on socalled ISP declarations we use for our ILP systems Tertius and 1BC,andthe term-based representation. We argue that the term-based representation does not have all the flexibility and expressiveness provided by the other representations

A Palimpsest Memory based on an

Capacity limited memory systems need to gradually forget old information in order to avoid catastrophic forgetting where all stored information is lost. This can be achieved by allowing new information to overwrite old, as in a so-called palimpsest memory. This paper describes a new such learning rule employed in an attractor neural network. The network does not exhibit catastrophic forgetting, has a capacity dependent on the learning time constant and exhibits recency eects in retrieval

. Summary of Results

This paper analyzes the aerial survey data from the Atlantic coast population only. Although McClenaghan and O'Shea (1988) provide genetic evidence that manatees from the east and west coasts of Florida intermingle, behavioral studies (e.g., Reid, Rathbun and Wilcox, 1991) suggest that such mixing is infrequent. closed (Reid, Rathbun and Wilcox, 1991). Because a standard survey protocol was not used prior to the 82-83 winter, only the data from that winter on are analyzed. For simplification, the seven site-specific counts at each survey are collapsed into two; the total of the two most northerly sites and the total of the remaining five. Table 1 summarizes the observed regional counts over the ten year period. Note the considerable variability among counts in each region and year. TABLE 1 HERE In addition to the counts themselves, several covariates were collected at each survey. Two covariates are the northern and southern water temperatures, each averaged over the two days prior to and the day of the survey. Also included is the total number of NOAA degree-days (number of air degrees below 6