# Difference between revisions of "MULTI-VIEW DATA GENERATION WITHOUT VIEW SUPERVISION"

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The Objective function for C-GMV will be: | The Objective function for C-GMV will be: | ||

− | <div style="text-align: center;font-size:100%"><math>\underset{G}{min} \ \underset{D}{max}</math> <math>E_{x_1,x_2 ~ p_x|l(x_1)=l(x_2)}[log D(x_1,x_2)] + E_{v_1,v_2~p_v,x_p_x}[log(1 − D(G(E(x),v_1),G(E(x),v_2)))] +E_{v∼p_v,x∼p_x}[log(1 − D(G(E(x), v), x)) </math></div> | + | <div style="text-align: center;font-size:100%"><math>\underset{G}{min} \ \underset{D}{max}</math> <math>E_{x_1,x_2 ~ p_x|l(x_1)=l(x_2)}[log D(x_1,x_2)] + E_{v_1,v_2~p_v,x_p_x}[log(1 − D(G(E(x),v_1),G(E(x),v_2)))] +E_{v∼p_v,x∼p_x}[log(1 − D(G(E(x), v), x))] </math></div> |

<div style="text-align: center;font-size:100%">[[File:CGMV.png]]</div> | <div style="text-align: center;font-size:100%">[[File:CGMV.png]]</div> |

## Revision as of 17:43, 8 November 2018

This page contains a summary of the paper "Multi-View Data Generation without Supervision" by Mickael Chen, Ludovic Denoyer, Thierry Artieres. It was published at the International Conference on Learning Representations (ICLR) in 2018 in Poster Category.

## Contents

## Introduction

### Motivation

High Dimensional Generative models have seen a surge of interest off late with introduction of Variational auto-encoders and generative adversarial networks. This paper focuses on a particular problem where one aims at generating samples corresponding to a number of objects under various views. The distribution of the data is assumed to be driven by two independent latent factors: the content, which represents the intrinsic features of an object, and the view, which stands for the settings of a particular observation of that object (for example, the different angles of the same object). The paper proposes two models using this disentanglement of latent space - a generative model and a conditional variant of the same.

### Related Work

The problem of handling multi-view inputs has mainly been studied from the predictive point of view where one wants, for example, to learn a model able to predict/classify over multiple views of the same object (Su et al. (2015); Qi et al. (2016)). These approaches generally involve (early or late) fusion of the different views at a particular level of a deep architecture. Recent studies have focused on identifying factors of variations from multiview datasets. The underlying idea is to consider that a particular data sample may be thought as the mix of a content information (e.g. related to its class label like a given person in a face dataset) and of a side information, the view, which accounts for factors of variability (e.g. exposure, viewpoint, with/wo glasses...). So, all the samples of same class contain the same content but different view. A number of approaches have been proposed to disentangle the content from the view, also referred as the style in some papers (Mathieu et al. (2016); Denton & Birodkar (2017)). The two common limitations the earlier approaches pose - as claimed by the paper - are that (i) they usually consider discrete views that are characterized by a domain or a set of discrete (binary/categorical) attributes (e.g. face with/wo glasses, the color of the hair, etc.) and could not easily scale to a large number of attributes or to continuous views. (ii) most models are trained using view supervision (e.g. the view attributes), which of course greatly helps learning such model, yet prevents their use on many datasets where this information is not available.

### Contributions

The contributions that authors claim are the following: (i) A new generative model able to generate data with various content and high view diversity using a supervision on the content information only. (ii) Extend the generative model to a conditional model that allows generating new views over any input sample.

## Paper Overview

### Background

The paper uses concept of the poplar GAN (Generative Adverserial Networks) proposed by Goodfellow et al.(2014).

GENERATIVE ADVERSARIAL NETWORK:

Generative adversarial networks (GANs) are deep neural net architectures comprised of two nets, pitting one against the other (thus the “adversarial”). GANs were introduced in a paper by Ian Goodfellow and other researchers at the University of Montreal, including Yoshua Bengio, in 2014. Referring to GANs, Facebook’s AI research director Yann LeCun called adversarial training “the most interesting idea in the last 10 years in ML.”

Let us denote [math]X[/math] an input space composed of multidimensional samples x e.g. vector, matrix or tensor. Given a latent space [math]R^n[/math] and a prior distribution [math]p_z(z)[/math] over this latent space, any generator function [math]G : R^n → X[/math] defines a distribution [math]p_G [/math] on [math] X[/math] which is the distribution of samples G(z) where [math]z ∼ p_z[/math]. A GAN defines, in addition to G, a discriminator function D : X → [0; 1] which aims at differentiating between real inputs sampled from the training set and fake inputs sampled following [math]p_G[/math], while the generator is learned to fool the discriminator D. Usually both G and D are implemented with neural networks. The objective function is based on the following adversarial criterion:

where px is the empirical data distribution on X . It has been shown in Goodfellow et al. (2014) that if G∗ and D∗ are optimal for the above criterion, the Jensen-Shannon divergence between [math]p_{G∗}[/math] and the empirical distribution of the data [math]p_x[/math] in the dataset is minimized, making GAN able to estimate complex continuous data distributions.

CONDITIONAL GENERATIVE ADVERSARIAL NETWORK:

In the Conditional GAN (CGAN), the generator learns to generate a fake sample with a specific condition or characteristics (such as a label associated with an image or more detailed tag) rather than a generic sample from unknown noise distribution. Now, to add such a condition to both generator and discriminator, we will simply feed some vector y, into both networks. Hence, both the discriminator D(X,y) and generator G(z,y) are jointly conditioned to two variables, z or X and y.

Now, the objective function of CGAN is:

The paper also suggests that, many studies have reported that on when dealing with high-dimensional input spaces, CGAN tends to collapse the modes of the data distribution,mostly ignoring the latent factor z and generating x only based on the condition y, exhibiting an almost deterministic behaviour.

### Generative Multi-View Model

** Objective and Notations: ** The distribution of the data x ∈ X is assumed to be driven by two latent factors: a content factor denoted c which corresponds to the invariant proprieties of the object,and a view factor denoted v which corresponds to the factor of variations. Typically, if X is the space of people’s faces, c stands for the intrinsic features of a person’s face while v stands for the transient features and the viewpoint of a particular photo of the face, including the photo exposure
and additional elements like a hat, glasses, etc.... These two factors c and v are assumed to be independent and these are the factors needed to learn.

The paper defines two tasks here to be done:
(i) **Multi View Generation**: we want to be able to sample over X by controlling the two factors c and v. Given two priors, p(c) and p(v), this sampling will be possible if we are able to estimate p(x|c, v) from a training set.
(ii) **Conditional Multi-View Generation**: the second objective is to be able to sample different views of a given object. Given a prior p(v), this sampling will be achieved by learning the probability p(c|x), in addition to p(x|c, v). Ability to learn generative models able to generate from a disentangled latent space would allow controlling the sampling on the two different axis,
the content and the view. The authors claim the originality of work is to learn such generative models without using any view labelling information.

** Generative Multi-view Model: **

Consider two prior distributions over the content and view factors denoted as [math]p_c[/math] and [math]pv[/math], corresponding to the prior distribution over content and latent factors. Moreover, we consider a generator G that implements a distribution over samples x, denoted as [math]p_G[/math] by computing G(c, v) with [math]c ∼ p_c[/math] and [math]v ∼ p_v[/math]. Objective is to learn this generator so that its first input c corresponds to the content of the generated sample while its second input v, captures the underlying view of the sample. Doing so would allow one to control the output sample of the generator by tuning its content or its view (i.e. c and v).

The key idea that authors propose is to focus on the distribution of pairs of inputs rather than on the distribution over individual samples. When no view supervision is available the only valuable pairs of samples that one may build from the dataset consist of two samples of a given object under two different views. When we choose any two samples randomly from the dataset from a same object, it is most likely that we get two different views. The paper explains that there are three goals here, (i) As in regular GAN, each sample generated by G needs to look realistic. (ii) As, real pairs are composed of two views of the same object, the generator should generate pairs of the same object. Since the two sampled view factors v1 and v2 are different, the only way this can be achieved is by encoding the content vector c which is invariant. (iii) It is expected that the discriminator should easily discriminate between a pair of samples corresponding to the same object under different views from a pair of samples corresponding to a same object under the same view. Because the pair shares the same content factor c, this should force the generator to use the view factors v1 and v2 to produce diversity in the generated pair.

Now, the objective function of GMV Model is:

Once the model is learned, generator G that generates single samples by first sampling c and v following [math]p_c[/math] and [math]p_v[/math], then by computing G(c, v). By freezing c or v, one may then generate samples corresponding to multiple views of any particular content, or corresponding to many contents under a particular view. One can also make interpolations between two given views over a particular content, or between two contents using a particular view

### Conditional Generative Model (C-GMV):

C-GMV is proposed by the authors to be able to change the view of a given object that would be provided as an input to the model.This model extends the generative model's the ability to extract the content factor from any given input and to use this extracted content in order to generate new views of the corresponding object. To achieve such a goal, we must add to our generative model an encoder function denoted [math]E : X → R^C[/math] that will map any input in X to the content space [math]R^C[/math]

Input sample x is encoded in the content space using an encoder function, noted E (implemented as a neural network). This encoder serves to generate a content vector c = E(x) that will be combined with a randomly sampled view [math]v ∼ p_v[/math] to generate an artificial example. The artificial sample is then combined with the original input x to form a negative pair. The issue with this approach is that CGAN are known to easily miss modes of the underlying distribution. The generator enters in a state where it ignores the noisy component v. To overcome this phenomenon, we use the same idea as in GMV. We build negative pairs [math](G(c, v_1), G(c, v_2))[/math] by randomly sampling two views [math]v_1[/math] and [math]v_2[/math] that are combined to get a unique content c. c is computed from a sample x using the encoder E, i.e. c= E(x). By doing so, the ability of our approach to generating pairs with view diversity is preserved. Since this diversity can only be captured by taking into account the two different view vectors provided to the model ([math]v_1[/math] and [math]v_2[/math]), this will encourage G(c, v) to generate samples containing both the content information c, and the view v. Positive pairs are sampled from the training set and correspond to two views of a given object.

The Objective function for C-GMV will be: