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Gupta, Shubham.
Deep Learning in *Rectified* *Gaussian* * Nets*.

Degree: Computer Science, 2018, University of California – San Diego

URL: http://www.escholarship.org/uc/item/8c3390fp

Here, we introduce a new family of probabilistic models called Rectified Gaussian Nets, or RGNs. RGNs can be thought of as an extension to Deep Boltzmann Machines (DBMs) with real non-negative nodes, instead of binary. Another distinguishing feature of RGN is that the probability density functions P(bf{it{y, h bar v}}) and P(bf{it{hbar v, y}}) are log-concave, even in deep architectures, where bf{it{v}} is the real valued input vector bounded between 0 and 1; bf{it{y}} and bf{it{h}} are the real valued output and hidden vectors respectively, rectified to be greater than or equal to zero. Due to this property, the most likely value of bf{it{y}} and bf{it{h}} conditioned on bf{it{v}} can be found exactly and efficiently, hence MAP estimate is tractable. We will also see that this property comes in handy, as the update rule for the network parameters resembles that of Boltzmann Machines, but we can approximate certain expectations over the nodes of the RGN by their MAP estimates, which is only a mild assumption as the posterior distribution over the nodes is provably unimodal. Hence, it is possible to train RGN both exactly and efficiently, unlike DBMs. We also show how one might go about using this model for generative modeling.

Subjects/Keywords: Computer science; deep boltzmann machines; Deep learning; Rectified Gaussian Nets

…probabilistic models called *Rectified* *Gaussian*
*Nets*, or RGNs. RGNs can be thought of as an extension… …call *rectified* *Gaussian* *Nets*, or RGNs.
1.1
Boltzmann Machines
A BM (Boltzmann Machine… …expertise and precious time.
viii
ABSTRACT OF THE THESIS
Deep Learning in *Rectified* *Gaussian*… …variables) which can be real and non-negative.
They model the data as a *rectified* *Gaussian*… …Chapter 2
*Rectified* *Gaussian* Network
In this chapter, we introduce a new architecture for deep…

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APA (6^{th} Edition):

Gupta, S. (2018). Deep Learning in Rectified Gaussian Nets. (Thesis). University of California – San Diego. Retrieved from http://www.escholarship.org/uc/item/8c3390fp

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Gupta, Shubham. “Deep Learning in Rectified Gaussian Nets.” 2018. Thesis, University of California – San Diego. Accessed January 25, 2020. http://www.escholarship.org/uc/item/8c3390fp.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Gupta, Shubham. “Deep Learning in Rectified Gaussian Nets.” 2018. Web. 25 Jan 2020.

Vancouver:

Gupta S. Deep Learning in Rectified Gaussian Nets. [Internet] [Thesis]. University of California – San Diego; 2018. [cited 2020 Jan 25]. Available from: http://www.escholarship.org/uc/item/8c3390fp.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Gupta S. Deep Learning in Rectified Gaussian Nets. [Thesis]. University of California – San Diego; 2018. Available from: http://www.escholarship.org/uc/item/8c3390fp

Not specified: Masters Thesis or Doctoral Dissertation