Geometry of the Restricted Boltzmann Machine Maŕıa
نویسندگان
چکیده
The restricted Boltzmann machine is a graphical model for binary random variables. Based on a complete bipartite graph separating hidden and observed variables, it is the binary analog to the factor analysis model. We study this graphical model from the perspectives of algebraic statistics and tropical geometry, starting with the observation that its Zariski closure is a Hadamard power of the first secant variety of the Segre variety of projective lines. We derive a dimension formula for the tropicalized model, and we use it to show that the restricted Boltzmann machine is identifiable in many cases. Our methods include coding theory and geometry of linear threshold functions.
منابع مشابه
A Hybrid Algorithm based on Deep Learning and Restricted Boltzmann Machine for Car Semantic Segmentation from Unmanned Aerial Vehicles (UAVs)-based Thermal Infrared Images
Nowadays, ground vehicle monitoring (GVM) is one of the areas of application in the intelligent traffic control system using image processing methods. In this context, the use of unmanned aerial vehicles based on thermal infrared (UAV-TIR) images is one of the optimal options for GVM due to the suitable spatial resolution, cost-effective and low volume of images. The methods that have been prop...
متن کاملApplication of continuous restricted Boltzmann machine to detect multivariate anomalies from stream sediment geochemical data, Korit, East of Iran
Anomaly separation using stream sediment geochemical data has an essential role in regional exploration. Many different techniques have been proposed to distinguish anomalous from study area. In this research, a continuous restricted Boltzmann machine (CRBM), which is a generative stochastic artificial neural network, was used to recognize the mineral potential area in Korit 1:100000 sheet, loc...
متن کاملGeometry of the Restricted Boltzmann Machine
The restricted Boltzmann machine is a graphical model for binary random variables. Based on a complete bipartite graph separating hidden and observed variables, it is the binary analog to the factor analysis model. We study this graphical model from the perspectives of algebraic statistics and tropical geometry, starting with the observation that its Zariski closure is a Hadamard power of the f...
متن کاملExternal and Internal Incompressible Viscous Flows Computation using Taylor Series Expansion and Least Square based Lattice Boltzmann Method
The lattice Boltzmann method (LBM) has recently become an alternative and promising computational fluid dynamics approach for simulating complex fluid flows. Despite its enormous success in many practical applications, the standard LBM is restricted to the lattice uniformity in the physical space. This is the main drawback of the standard LBM for flow problems with complex geometry. Several app...
متن کاملUniversal Approximation Results for the Temporal Restricted Boltzmann Machine and the Recurrent Temporal Restricted Boltzmann Machine
The Restricted Boltzmann Machine (RBM) has proved to be a powerful tool in machine learning, both on its own and as the building block for Deep Belief Networks (multi-layer generative graphical models). The RBM and Deep Belief Network have been shown to be universal approximators for probability distributions on binary vectors. In this paper we prove several similar universal approximation resu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009