Algorithm Portfolios for Noisy Optimization

Noisy optimization is the optimization of objective functions corrupted by noise. A portfolio of solvers is a set of solvers equipped with an algorithm selection tool for distributing the computational power among them. Portfolios are widely and successfully used in combinatorial optimization. In this work, we study portfolios of noisy optimization solvers. We obtain mathematically proved performance (in the sense that the portfolio performs nearly as well as the best of its solvers) by an ad hoc portfolio algorithm dedicated to noisy optimization. A somehow surprising result is that it is better to compare solvers with some lag, i.e., propose the current recommendation of best solver based on their performance earlier in the run. An additional finding is a principled method for distributing the computational power among solvers in the portfolio.Comment: in Annals of Mathematics and Artificial Intelligence, Springer Verlag, 201

Sensitivity And Out-Of-Sample Error in Continuous Time Data Assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time--tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established which allows to calculate the latter under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, aka synchronisation. Numerical examples demonstrate the feasibility of the approach.Comment: submitted to Quarterly Journal of the Royal Meteorological Societ

Edge-weighting of gene expression graphs

In recent years, considerable research efforts have been directed to micro-array technologies and their role in providing simultaneous information on expression profiles for thousands of genes. These data, when subjected to clustering and classification procedures, can assist in identifying patterns and providing insight on biological processes. To understand the properties of complex gene expression datasets, graphical representations can be used. Intuitively, the data can be represented in terms of a bipartite graph, with weighted edges corresponding to gene-sample node couples in the dataset. Biologically meaningful subgraphs can be sought, but performance can be influenced both by the search algorithm, and, by the graph-weighting scheme and both merit rigorous investigation. In this paper, we focus on edge-weighting schemes for bipartite graphical representation of gene expression. Two novel methods are presented: the first is based on empirical evidence; the second on a geometric distribution. The schemes are compared for several real datasets, assessing efficiency of performance based on four essential properties: robustness to noise and missing values, discrimination, parameter influence on scheme efficiency and reusability. Recommendations and limitations are briefly discussed

A determination of the molar gas constant R by acoustic thermometry in helium

We have determined the acoustic and microwave frequencies of a misaligned spherical resonator maintained near the temperature of the triple point of water and filled with helium with carefully characterized molar mass M = (4.002 6032 ± 0.000 0015) g mol-1, with a relative standard uncertainty ur(M) = 0.37×10-6. From these data and traceable thermometry we estimate the speed of sound in our sample of helium at TTPW = 273.16 K and zero pressure to be u0 2 = (945 710.45 ± 0.85) m2 s-2 and correspondingly deduce the value R = (8.314 4743 ± 0.000 0088) J mol-1 K-1 for the molar gas constant. We estimate the value k = R/NA = (1.380 6508 ± 0.000 0015) × 10-23 J K-1 for the Boltzmann constant using the currently accepted value of the Avogadro constant NA. These estimates of R and k, with a relative standard uncertainty of 1.06 × 10-6, are 1.47 parts in 106 above the values recommended by CODATA in 2010

Robust Recommender System: A Survey and Future Directions

With the rapid growth of information, recommender systems have become integral for providing personalized suggestions and overcoming information overload. However, their practical deployment often encounters "dirty" data, where noise or malicious information can lead to abnormal recommendations. Research on improving recommender systems' robustness against such dirty data has thus gained significant attention. This survey provides a comprehensive review of recent work on recommender systems' robustness. We first present a taxonomy to organize current techniques for withstanding malicious attacks and natural noise. We then explore state-of-the-art methods in each category, including fraudster detection, adversarial training, certifiable robust training against malicious attacks, and regularization, purification, self-supervised learning against natural noise. Additionally, we summarize evaluation metrics and common datasets used to assess robustness. We discuss robustness across varying recommendation scenarios and its interplay with other properties like accuracy, interpretability, privacy, and fairness. Finally, we delve into open issues and future research directions in this emerging field. Our goal is to equip readers with a holistic understanding of robust recommender systems and spotlight pathways for future research and development