Probability and Statistics explained in the context of deep learning


This article is intended for beginners in deep learning who wish to gain knowledge about probability and statistics and also as a reference for practitioners. In my previous article, I wrote about the concepts of linear algebra for deep learning in a top down approach ( link for the article) (If you do not have enough idea about linear algebra, please read that first).The same top down approach is used here.Providing the description of use cases first and then the concepts. All the example code uses python and numpy.Formulas are provided as images for reuse. Probability is the science of quantifying uncertain things.Most of machine learning and deep learning systems utilize a lot of data to learn about patterns in the data.Whenever data is utilized in a system rather than sole logic, uncertainty grows up and whenever uncertainty grows up, probability becomes relevant. By introducing probability to a deep learning system, we introduce common sense to the system.Otherwise the system would be very brittle and will not be useful.In deep learning, several models like bayesian models, probabilistic graphical models, hidden markov models are used.They depend entirely on probability concepts.

Gaussian-binary Restricted Boltzmann Machines on Modeling Natural Image Statistics Machine Learning

We present a theoretical analysis of Gaussian-binary restricted Boltzmann machines (GRBMs) from the perspective of density models. The key aspect of this analysis is to show that GRBMs can be formulated as a constrained mixture of Gaussians, which gives a much better insight into the model's capabilities and limitations. We show that GRBMs are capable of learning meaningful features both in a two-dimensional blind source separation task and in modeling natural images. Further, we show that reported difficulties in training GRBMs are due to the failure of the training algorithm rather than the model itself. Based on our analysis we are able to propose several training recipes, which allowed successful and fast training in our experiments. Finally, we discuss the relationship of GRBMs to several modifications that have been proposed to improve the model.

Performance Impact Caused by Hidden Bias of Training Data for Recognizing Textual Entailment Artificial Intelligence

The quality of training data is one of the crucial problems when a learning-centered approach is employed. This paper proposes a new method to investigate the quality of a large corpus designed for the recognizing textual entailment (RTE) task. The proposed method, which is inspired by a statistical hypothesis test, consists of two phases: the first phase is to introduce the predictability of textual entailment labels as a null hypothesis which is extremely unacceptable if a target corpus has no hidden bias, and the second phase is to test the null hypothesis using a Naive Bayes model. The experimental result of the Stanford Natural Language Inference (SNLI) corpus does not reject the null hypothesis. Therefore, it indicates that the SNLI corpus has a hidden bias which allows prediction of textual entailment labels from hypothesis sentences even if no context information is given by a premise sentence. This paper also presents the performance impact of NN models for RTE caused by this hidden bias.

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