Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Lévy processes and infinitely divisible distributions

Harmonic Analysis and the Theory of Probability. By S. Bochner pp. 176. 35s. 1955. (California University Press and Cambridge University Press)

Deep Neural Networks trained as image auto-encoders have recently emerged as a promising direction for advancing the state-of-the-art in image compression. The key challenge in learning such networks is twofold: To deal with quantization, and to control the trade-off between reconstruction error (distortion) and entropy (rate) of the latent image representation. In this paper, we focus on the latter challenge and propose a new technique to navigate the rate-distortion trade-off for an image compression auto-encoder. The main idea is to directly model the entropy of the latent representation by using a context model: A 3D-CNN which learns a conditional probability model of the latent distribution of the auto-encoder. During training, the auto-encoder makes use of the context model to estimate the entropy of its representation, and the context model is concurrently updated to learn the dependencies between the symbols in the latent representation. Our experiments show that this approach, when measured in MS-SSIM, yields a state-of-the-art image compression system based on a simple convolutional auto-encoder.

/pdf/conditional-probability-models-for-deep-image-compression-52lqbky8lh.pdf

Conditional Probability Models for Deep Image Compression

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Principles Of Random Walk

This is lecture notes on the course "Stochastic Processes". In this format, the course was taught in the spring semesters 2017 and 2018 for third-year bachelor students of the Department of Control and Applied Mathematics, School of Applied Mathematics and Informatics at Moscow Institute of Physics and Technology. The base of this course was formed and taught for decades by professors from the Department of Mathematical Foundations of Control A.A. Natan, S.A. Guz, and O.G. Gorbachev. 
Besides standard chapters of stochastic processes theory (correlation theory, Markov processes) in this book (and lectures) the following chapters are included: von Neumann-Birkhoff-Khinchin ergodic theorem, macrosystem equilibrium concept, Markov Chain Monte Carlo, Markov decision processes and the secretary problem.

Lecture Notes on Stochastic Processes

/pdf/the-global-rate-of-convergence-for-optimal-tensor-methods-in-2ktlbxoufu.pdf

The global rate of convergence for optimal tensor methods in smooth convex optimization

For the critical branching random walk on the lattice Zd, in the case of an arbitrary total number of produced offspring spreading on the lattice from the parental particle, the existence o...

Steady state and intermittency in the critical branching random walk with arbitrary total number of offspring

The main goal in this paper is to propose a new approach to deriving oracle inequalities related to the exponential weighting method. The paper focuses on recovering an unknown vector from noisy data with the help of the family of ordered smoothers [12]. The estimators withing this family are aggregated using the exponential weighting method and the aim is to control the risk of the aggregated estimate. Based on the natural probabilistic properties of the unbiased risk estimate, we derive new oracle inequalities for the mean square risk and show that the exponential weighting permits to improve Kneip’s oracle inequality.

/pdf/ordered-smoothers-with-exponential-weighting-vfthqioqbo.pdf

Ordered smoothers with exponential weighting

In a population model in continuous space, individuals evolve independently as branching random walks subject to immigration. If the underlying branching mechanism is subcritical, the model has a u...

/pdf/population-model-with-immigration-in-continuous-space-52cly04m1g.pdf

Elena Chernousova

Papers

Lecture Notes on Stochastic Processes

The global rate of convergence for optimal tensor methods in smooth convex optimization

Steady state and intermittency in the critical branching random walk with arbitrary total number of offspring

Ordered smoothers with exponential weighting

Population model with immigration in continuous space