A few months ago, I built a recommender system that employed topic modelling to display relevant tasks to employees. The algorithm used was Latent Dirichlet Allocation (LDA), a generative model that has been around since the early 2000s¹. Of course, I didn't rewrite LDA from scratch but used the implementation in Python's scikit-learn. But it started me thinking about the sequence of research that lead to the creation of the LDA model. The problem with such libraries is that it's all too easy to include a few lines in your code and just move on, so I dug out my old machine learning books with the goal of knowing enough to be able to explain LDA in all its gory probabilistic detail.
Although quantities such as the mean, the variance, and possibly higher order moments of a random variable have often been sufficient to characterize a particular problem, the quest for higher modeling accuracy, and for more realistic assumptions drives us towards modeling the available random variables using their probability density. This of course leads us to the problem of density estimation (see ). The most common approach for density estimation is the nonparametric approach, where the density is determined according to a formula involving the data points available. The most common non parametric methods are the kernel density estimator, alsoknown as the Parzen window estimator  and the k-nearest neighbor technique . Non parametric density estimation belongs to the class of ill-posed problems in the sense that small changes in the data can lead to large changes in "To whom correspondence should be addressed.
Probability Distribution is an important topic that each data scientist should know for the analysis of the data. It defines all the related possibility outcomes of a variable. In this, the article you will understand all the Probability Distribution types that help you to determine the distribution for the dataset. There are two types of distribution. In the discrete Distribution, the sum of the probabilities of all the individuals is equal to one.
Having a sound statistical background can be greatly beneficial in the daily life of a Data Scientist. Every time we start exploring a new dataset, we need to first do an Exploratory Data Analysis (EDA) in order to get a feeling of what are the main characteristics of certain features. If we are able to understand if it's present any pattern in the data distribution, we can then tailor-made our Machine Learning models to best fit our case study. In this way, we will be able to get a better result in less time (reducing the optimisation steps). In fact, some Machine Learning models are designed to work best under some distribution assumptions.
The probability density function for the visible sector of a Riemann-Theta Boltzmann machine can be taken conditional on a subset of the visible units. We derive that the corresponding conditional density function is given by a reparameterization of the Riemann-Theta Boltzmann machine modelling the original probability density function. Therefore the conditional densities can be directly inferred from the Riemann-Theta Boltzmann machine.