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Contours of a bivariate normal distribution

Bivariate normal distribution – explicit reconstruction of a BVD random vector via Cholesky decomposition of the covariance matrix

In other posts of this blog I have discussed the general form of a Bivariate Normal Distribution [BVD] . For a centered Cartesian coordinate system [CCS] (see below), we have already seen the following: In this post I will give you a recipe to explicitly construct two random variables X, Y of a BVD from 1-dimensional Gaussians Z1, Z2 with… Read More »Bivariate normal distribution – explicit reconstruction of a BVD random vector via Cholesky decomposition of the covariance matrix

Bivariate Normal Distribution

Bivariate normal distribution – derivation by linear transformation of a random vector of two independent Gaussians

In an another post on properties of a Bivariate Normal Distribution [BVD] I have motivated the form of its probability density function [pdf] by symmetry arguments and the underlying probability density functions of its marginals, namely 1-dimensional Gaussians. In this post we will derive the probability density function by following the line of argumentation for a general Multivariate Normal Distribution… Read More »Bivariate normal distribution – derivation by linear transformation of a random vector of two independent Gaussians

Performance comparison of PyTorch and Keras3 with TF2 and Torch backends for a small NN-model on a Nvidia 4060 TI – II – Keras with Torch backend

Not all tasks in Machine Learning [ML] require big LLMs or LLM-based interfaces. Actually, many interesting ML-tasks can be solved with neural networks [NNs] that fit well into the VRAM of a modern GPU or TPU affordable even for private persons. This statements holds in particular for image processing. We have groups of people either learning to work with ML… Read More »Performance comparison of PyTorch and Keras3 with TF2 and Torch backends for a small NN-model on a Nvidia 4060 TI – II – Keras with Torch backend

Performance of PyTorch vs. Keras 3 with tensorflow/torch backends for a small NN-model on a Nvidia 4060 TI – I – Torch vs. Keras3/TF2 and relevant parameters

Today’s world of Machine Learning is characterized by competing frameworks. I am used to the combination of Keras with the Tensorflow2 [TF2] backend, but have turned now to using PyTorch in addition. As a beginner with PyTorch, I wanted to get an impression about potential performance advantages in comparison with the Keras/TF2 framework combination. I had read about significant performance… Read More »Performance of PyTorch vs. Keras 3 with tensorflow/torch backends for a small NN-model on a Nvidia 4060 TI – I – Torch vs. Keras3/TF2 and relevant parameters