Evgeny Burnaev

Regression on the basis of nonstationary Gaussian processes with Bayesian regularization

We consider the regression problem, i.e. prediction of a real valued function. A Gaussian process prior is imposed on the function, and is combined with the training data to obtain predictions for new points. We introduce a Bayesian regularization on parameters of a covariance function of the process, which increases quality of approximation and robustness of the estimation. Also an approach to modeling nonstationary covariance function of a Gaussian process on basis of linear expansion in parametric functional dictionary is proposed. Introducing such a covariance function allows to model functions, which have non-homogeneous behaviour. Combining above features with careful optimization of covariance function parameters results in unified approach, which can be easily implemented and applied. The resulting algorithm is an out of the box solution to regression problems, with no need to tune parameters manually. The effectiveness of the method is demonstrated on various datasets.

Computationally efficient algorithm for Gaussian Process regression in case of structured samples

Surrogate modeling is widely used in many engineering problems. Data sets often have Cartesian product structure (for instance factorial design of experiments with missing points). In such case the size of the data set can be very large. Therefore, one of the most popular algorithms for approximation–Gaussian Process regression–can be hardly applied due to its computational complexity. In this paper a computationally efficient approach for constructing Gaussian Process regression in case of data sets with Cartesian product structure is presented. Efficiency is achieved by using a special structure of the data set and operations with tensors. Proposed algorithm has low computational as well as memory complexity compared to existing algorithms. In this work we also introduce a regularization procedure allowing to take into account anisotropy of the data set and avoid degeneracy of regression model.

Ensembles of detectors for online detection of transient changes

Classical change-point detection procedures assume a change-point model to be known and a change consisting in establishing a new observations regime, i.e. the change lasts infinitely long. These modeling assumptions contradicts applied problems statements. Therefore, even theoretically optimal statistics in practice very often fail when detecting transient changes online. In this work in order to overcome limitations of classical change-point detection procedures we consider approaches to constructing ensembles of change-point detectors, i.e. algorithms that use many detectors to reliably identify a change-point. We propose a learning paradigm and specific implementations of ensembles for change detection of short-term (transient) changes in observed time series. We demonstrate by means of numerical experiments that the performance of an ensemble is superior to that of the conventional change-point detection procedures.

Surrogate modeling of multifidelity data for large samples

The problem of construction of a surrogate model based on available lowand high-fidelity data is considered. The low-fidelity data can be obtained, e.g., by performing the computer simulation and the high-fidelity data can be obtained by performing experiments in a wind tunnel. A regression model based on Gaussian processes proves to be convenient for modeling variable-fidelity data. Using this model, one can efficiently reconstruct nonlinear dependences and estimate the prediction accuracy at a specified point. However, if the sample size exceeds several thousand points, direct use of the Gaussian process regression becomes impossible due to a high computational complexity of the algorithm. We develop new algorithms for processing multifidelity data based on Gaussian process model, which are efficient even for large samples. We illustrate application of the developed algorithms by constructing surrogate models of a complex engineering system.

Efficient design of experiments for sensitivity analysis based on polynomial chaos expansions

Global sensitivity analysis aims at quantifying respective effects of input random variables (or combinations thereof) onto variance of a physical or mathematical model response. Among the abundant literature on sensitivity measures, Sobol indices have received much attention since they provide accurate information for most of models. We consider a problem of experimental design points selection for Sobol’ indices estimation. Based on the concept of D-optimality, we propose a method for constructing an adaptive design of experiments, effective for calculation of Sobol’ indices based on Polynomial Chaos Expansions. We provide a set of applications that demonstrate the efficiency of the proposed approach.

Model Selection for Anomaly Detection

Anomaly detection based on one-class classification algorithms is broadly used in many applied domains like image processing (e.g. detection of whether a patient is “cancerous” or “healthy” from mammography image), network intrusion detection, etc. Performance of an anomaly detection algorithm crucially depends on a kernel, used to measure similarity in a feature space. The standard approaches (e.g. cross-validation) for kernel selection, used in two-class classification problems, can not be used directly due to the specific nature of a data (absence of a second, abnormal, class data). In this paper we generalize several kernel selection methods from binary-class case to the case of one-class classification and perform extensive comparison of these approaches using both synthetic and real-world data.

Application of sorting and next generation sequencing to study 5′-UTR influence on translation efficiency in Escherichia coli

Abstract Yield of protein per translated mRNA may vary by four orders of magnitude. Many studies analyzed the influence of mRNA features on the translation yield. However, a detailed understanding of how mRNA sequence determines its propensity to be translated is still missing. Here, we constructed a set of reporter plasmid libraries encoding CER fluorescent protein preceded by randomized 5΄ untranslated regions (5΄-UTR) and Red fluorescent protein (RFP) used as an internal control. Each library was transformed into Escherchia coli cells, separated by efficiency of CER mRNA translation by a cell sorter and subjected to next generation sequencing. We tested efficiency of translation of the CER gene preceded by each of 48 natural 5΄-UTR sequences and introduced random and designed mutations into natural and artificially selected 5΄-UTRs. Several distinct properties could be ascribed to a group of 5΄-UTRs most efficient in translation. In addition to known ones, several previously unrecognized features that contribute to the translation enhancement were found, such as low proportion of cytidine residues, multiple SD sequences and AG repeats. The latter could be identified as translation enhancer, albeit less efficient than SD sequence in several natural 5΄-UTRs.

Nonparametric decomposition of quasi-periodic time series for change-point detection

The paper is concerned with the sequential online change-point detection problem for a dynamical system driven by a quasiperiodic stochastic process. We propose a multicomponent time series model and an effective online decomposition algorithm to approximate the components of the models. Assuming the stationarity of the obtained components, we approach the change-point detection problem on a per-component basis and propose two online change-point detection schemes corresponding to two real-world scenarios. Experimental results for decomposition and detection algorithms for synthesized and real-world datasets are provided to demonstrate the efficiency of our change-point detection framework.

Influence of resampling on accuracy of imbalanced classification

In many real-world binary classification tasks (e.g. detection of certain objects from images), an available dataset is imbalanced, i.e., it has much less representatives of a one class (a minor class), than of another. Generally, accurate prediction of the minor class is crucial but it’s hard to achieve since there is not much information about the minor class. One approach to deal with this problem is to preliminarily resample the dataset, i.e., add new elements to the dataset or remove existing ones. Resampling can be done in various ways which raises the problem of choosing the most appropriate one. In this paper we experimentally investigate impact of resampling on classification accuracy, compare resampling methods and highlight key points and difficulties of resampling.

Large-Scale Shape Retrieval with Sparse 3D Convolutional Neural Networks

In this paper we present results of performance evaluation of S3DCNN - a Sparse 3D Convolutional Neural Network - on a large-scale 3D Shape benchmark ModelNet40, and measure how it is impacted by voxel resolution of input shape. We demonstrate comparable classification and retrieval performance to state-of-the-art models, but with much less computational costs in training and inference phases. We also notice that benefits of higher input resolution can be limited by an ability of a neural network to generalize high level features.