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ICA based on Split Generalized Gaussian

Spurek Przemysław, Rola Przemysław, Tabor Jacek, Czechowski Aleksander, Bedychaj Andrzej

Schedae Informaticae

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2019

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Vol. 28

25--47

EN

Independent Component Analysis (ICA) is a method for searching the linear transformation that minimizes the statistical dependence between its components. Most popular ICA methods use kurtosis as a metric of independence (non-Gaussianity) to maximize, such as FastICA and JADE. However, their assumption of fourth-order moment (kurtosis) may not always be satisfied in practice. One of the possible solution is to use third-order moment (skewness) instead of kurtosis, which was applied in ICASG and EcoICA. In this paper we present a competitive approach to ICA based on the Split Generalized Gaussian distribution (SGGD), which is well adapted to heavy-tailed as well as asymmetric data. Consequently, we obtain a method which works better than the classical approaches, in both cases: heavy tails and non-symmetric data.

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Sliced Generative Models

Knop Szymon, Mazur Marcin, Tabor Jacek, Podolak Igor T., Spurek Przemysław

Schedae Informaticae

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2018

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Vol. 27

69--79

EN

In this paper we discuss a class of AutoEncoder based generative models based on one dimensional sliced approach. The idea is based on the reduction of the discrimination between samples to one-dimensional case. Our experiments show that methods can be divided into two groups. First consists of methods which are a modification of standard normality tests, while the second is based on classical distances between samples. It turns out that both groups are correct generative models, but the second one gives a slightly faster decrease rate of Fréchet Inception Distance (FID).

3

lossgrad : Automatic Learning Rate in Gradient Descent

Wójcik Bartosz, Maziarka Łukasz, Tabor Jacek

Schedae Informaticae

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2018

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Vol. 27

47--57

EN

In this paper, we propose a simple, fast and easy to implement algorithm lossgrad (locally optimal step-size in gradient descent), which au- tomatically modifies the step-size in gradient descent during neural networks training. Given a function f, a point x, and the gradient rxf of f, we aim to nd the step-size h which is (locally) optimal, i.e. satisfies: h = arg min t0 f(x 􀀀 trxf): Making use of quadratic approximation, we show that the algorithm satisfies the above assumption. We experimentally show that our method is insensitive to the choice of initial learning rate while achieving results comparable to other methods.

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Image stitching based on entropy minimizationI

Misztal Krzysztof, Spurek Przemysław, Tabor Jacek

Schedae Informaticae

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2018

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Vol. 27

EN

In this paper we present a method with closed analytic formula of stitching aligned images. It is obtained by choosing a statistically optimal global color change of one part of image. This approach, due to its numerical efficiency, is especially well-suited for merging big amount of satellite images into a single map. Moreover, we present solution of a general problem, how to find an optimal shift by v of data Y with respect to v from V, so that the dataset X, Y+v is maximally statistically consistent. We show that the solution is given in a closed analytic form.