In recent years, supervised learning with convolutional networks (CNNs) has seen huge adoption in computer vision applications. Comparatively, unsupervised learning with CNNs has received less attention. In this work we hope to help bridge the gap between the success of CNNs for supervised learning and unsupervised learning. We introduce a class of CNNs called deep convolutional generative adversarial networks (DCGANs), that have certain architectural constraints, and demonstrate that they are a strong candidate for unsupervised learning. Training on various image datasets, we show convincing evidence that our deep convolutional adversarial pair learns a hierarchy of representations from object parts to scenes in both the generator and discriminator. Additionally, we use the learned features for novel tasks - demonstrating their applicability as general image representations.

Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks

Recent advances in convolutional neural networks

中枢神経系疾患の治療は正常細胞（ニューロン）の機能維持を目的とするが，脳血管障害のように機能障害の原因が細胞の死滅に基づくことは多い．一方，脳腫瘍の治療においては薬物療法や放射線療法といった腫瘍細胞の死滅を目標とするものが大きな位置を占める．いずれの場合にも，細胞死の機序を理解することは各種病態や治療法の理解のうえで重要である．現在のところ最も研究の進んでいる細胞死の型はアポトーシスである．そのなかで重要な位置を占めるミトコンドリアにおける反応および抗アポトーシス因子について概要を紹介する．

Neuroscience 細胞死：最近の知見

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

Matrix Differential Calculus with Applications in Statistics and Econometrics

GNU Octave manual version 3: a high-level interactive language for numerical computations

Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator imply that the latent space gives a distorted view of the input space. Under mild conditions, we show that this distortion can be characterized by a stochastic Riemannian metric, and demonstrate that distances and interpolants are significantly improved under this metric. This in turn improves probability distributions, sampling algorithms and clustering in the latent space. Our geometric analysis further reveals that current generators provide poor variance estimates and we propose a new generator architecture with vastly improved variance estimates. Results are demonstrated on convolutional and fully connected variational autoencoders, but the formalism easily generalize to other deep generative models.

/pdf/latent-space-oddity-on-the-curvature-of-deep-generative-362q7oy2qk.pdf

Latent space oddity: On the curvature of deep generative models

This manual is the definitive guide to GNU Octave, an interactive environment for numerical computation. GNU Octave provides a convenient command-line interface for solving linear and nonlinear problems using vectors and matrices. This updated edition of the manual covers version 3 of GNU Octave, and includes documentation for new features such as sparse matrices, linear programming and computational geometry.GNU Octave is free software, distributed under the GNU General Public License (GPL). All the money raised from the sale of this book supports the development of free software. For each copy sold $1 will be donated to the GNU Octave Development Fund.About the authors: John W. Eaton is the original developer of GNU Octave.

GNU Octave Manual Version 3

Data augmentation is a key element in training high-dimensional models. In this approach, one synthesizes new observations by applying pre-specified transformations to the original training data; e.g.~new images are formed by rotating old ones. Current augmentation schemes, however, rely on manual specification of the applied transformations, making data augmentation an implicit form of feature engineering. With an eye towards true end-to-end learning, we suggest learning the applied transformations on a per-class basis. Particularly, we align image pairs within each class under the assumption that the spatial transformation between images belongs to a large class of diffeomorphisms. We then learn a class-specific probabilistic generative models of the transformations in a Riemannian submanifold of the Lie group of diffeomorphisms. We demonstrate significant performance improvements in training deep neural nets over manually-specified augmentation schemes. Our code and augmented datasets are available online.

/pdf/dreaming-more-data-class-dependent-distributions-over-44i0ho9pkw.pdf

Dreaming More Data: Class-dependent Distributions over Diffeomorphisms for Learned Data Augmentation

Manifolds are widely used to model non-linearity arising in a range of computer vision applications. This paper treats statistics on manifolds and the loss of accuracy occurring when linearizing the manifold prior to performing statistical operations. Using recent advances in manifold computations, we present a comparison between the non-linear analog of Principal Component Analysis, Principal Geodesic Analysis, in its linearized form and its exact counterpart that uses true intrinsic distances. We give examples of datasets for which the linearized version provides good approximations and for which it does not. Indicators for the differences between the two versions are then developed and applied to two examples of manifold valued data: outlines of vertebrae from a study of vertebral fractures and spacial coordinates of human skeleton end-effectors acquired using a stereo camera and tracking software.

/pdf/manifold-valued-statistics-exact-principal-geodesic-analysis-56s01wx85h.pdf

Søren Hauberg

Papers

GNU Octave manual version 3: a high-level interactive language for numerical computations

Latent space oddity: On the curvature of deep generative models

GNU Octave Manual Version 3

Dreaming More Data: Class-dependent Distributions over Diffeomorphisms for Learned Data Augmentation

Manifold valued statistics, exact principal, geodesic analysis and the effect of linear, approximations