arXiv subjects

Maxim Panov

Publications and source records attributed to Maxim Panov.

63 records · Page 4Linked to original sources

arXiv2019

Geometry-Aware Maximum Likelihood Estimation of Intrinsic Dimension

The existing approaches to intrinsic dimension estimation usually are not reliable when the data are nonlinearly embedded in the high dimensional space. In this work, we show that the explicit accounting to geometric properties of unknown support leads to the polynomial correction to the standard maximum likelihood estimate of intrinsic dimension for flat manifolds. The proposed algorithm (GeoMLE) realizes the correction by regression of standard MLEs based on distances to nearest neighbors for different sizes of neighborhoods. Moreover, the proposed approach also efficiently handles the case of nonuniform sampling of the manifold. We perform numerous experiments on different synthetic and real-world datasets. The results show that our algorithm achieves state-of-the-art performance, while also being computationally efficient and robust to noise in the data.

stat.ML↗

arXiv2019

Deeper Connections between Neural Networks and Gaussian Processes Speed-up Active Learning

Active learning methods for neural networks are usually based on greedy criteria which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one active learning iteration, or retraining the neural network after adding each data point, which is computationally inefficient. Moreover, uncertainty estimates for neural networks sometimes are overconfident for the points lying far from the training sample. In this work we propose to approximate Bayesian neural networks (BNN) by Gaussian processes, which allows us to update the uncertainty estimates of predictions efficiently without retraining the neural network, while avoiding overconfident uncertainty prediction for out-of-sample points. In a series of experiments on real-world data including large-scale problems of chemical and physical modeling, we show superiority of the proposed approach over the state-of-the-art methods.

cs.LG↗

arXiv2018

Sparse Group Inductive Matrix Completion

We consider the problem of matrix completion with side information (\textit{inductive matrix completion}). In real-world applications many side-channel features are typically non-informative making feature selection an important part of the problem. We incorporate feature selection into inductive matrix completion by proposing a matrix factorization framework with group-lasso regularization on side feature parameter matrices. We demonstrate, that the theoretical sample complexity for the proposed method is much lower compared to its competitors in sparse problems, and propose an efficient optimization algorithm for the resulting low-rank matrix completion problem with sparsifying regularizers. Experiments on synthetic and real-world datasets show that the proposed approach outperforms other methods.

stat.ML↗

arXiv2018

Constructing Graph Node Embeddings via Discrimination of Similarity Distributions

The problem of unsupervised learning node embeddings in graphs is one of the important directions in modern network science. In this work we propose a novel framework, which is aimed to find embeddings by \textit{discriminating distributions of similarities (DDoS)} between nodes in the graph. The general idea is implemented by maximizing the \textit{earth mover distance} between distributions of decoded similarities of similar and dissimilar nodes. The resulting algorithm generates embeddings which give a state-of-the-art performance in the problem of link prediction in real-world graphs.

stat.ML↗

arXiv2018

Dropout-based Active Learning for Regression

Active learning is relevant and challenging for high-dimensional regression models when the annotation of the samples is expensive. Yet most of the existing sampling methods cannot be applied to large-scale problems, consuming too much time for data processing. In this paper, we propose a fast active learning algorithm for regression, tailored for neural network models. It is based on uncertainty estimation from stochastic dropout output of the network. Experiments on both synthetic and real-world datasets show comparable or better performance (depending on the accuracy metric) as compared to the baselines. This approach can be generalized to other deep learning architectures. It can be used to systematically improve a machine-learning model as it offers a computationally efficient way of sampling additional data.

cs.LG↗

arXiv2017

Simultaneous Matrix Diagonalization for Structural Brain Networks Classification

This paper considers the problem of brain disease classification based on connectome data. A connectome is a network representation of a human brain. The typical connectome classification problem is very challenging because of the small sample size and high dimensionality of the data. We propose to use simultaneous approximate diagonalization of adjacency matrices in order to compute their eigenstructures in more stable way. The obtained approximate eigenvalues are further used as features for classification. The proposed approach is demonstrated to be efficient for detection of Alzheimer's disease, outperforming simple baselines and competing with state-of-the-art approaches to brain disease classification.

stat.ML↗

arXiv2017

Consistent Estimation of Mixed Memberships with Successive Projections

This paper considers the parameter estimation problem in Mixed Membership Stochastic Block Model (MMSB), which is a quite general instance of random graph model allowing for overlapping community structure. We present the new algorithm successive projection overlapping clustering (SPOC) which combines the ideas of spectral clustering and geometric approach for separable non-negative matrix factorization. The proposed algorithm is provably consistent under MMSB with general conditions on the parameters of the model. SPOC is also shown to perform well experimentally in comparison to other algorithms.

math.ST↗

arXiv2016

GTApprox: surrogate modeling for industrial design

We describe GTApprox - a new tool for medium-scale surrogate modeling in industrial design. Compared to existing software, GTApprox brings several innovations: a few novel approximation algorithms, several advanced methods of automated model selection, novel options in the form of hints. We demonstrate the efficiency of GTApprox on a large collection of test problems. In addition, we describe several applications of GTApprox to real engineering problems.

cs.MS↗

arXiv2014

Finite Sample Bernstein -- von Mises Theorem for Semiparametric Problems

The classical parametric and semiparametric Bernstein -- von Mises (BvM) results are reconsidered in a non-classical setup allowing finite samples and model misspecification. In the case of a finite dimensional nuisance parameter we obtain an upper bound on the error of Gaussian approximation of the posterior distribution for the target parameter which is explicit in the dimension of the nuisance and target parameters. This helps to identify the so called \emph{critical dimension} $ p $ of the full parameter for which the BvM result is applicable. In the important i.i.d. case, we show that the condition "$ p^{3} / n $ is small" is sufficient for BvM result to be valid under general assumptions on the model. We also provide an example of a model with the phase transition effect: the statement of the BvM theorem fails when the dimension $ p $ approaches $ n^{1/3} $. The results are extended to the case of infinite dimensional parameters with the nuisance parameter from a Sobolev class. In particular we show near normality of the posterior if the smoothness parameter $s$ exceeds 3/2.

math.ST↗