Added engery based model paper

README.md

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 ## List of papers
 
+* [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://shagunsodhani.com/papers-I-read/Your-Classifier-is-Secretly-an-Energy-Based-Model,-and-You-Should-Treat-it-Like-One)
 * [Massively Multilingual Neural Machine Translation in the Wild - Findings and Challenges](https://shagunsodhani.com/papers-I-read/Massively-Multilingual-Neural-Machine-Translation-in-the-Wild-Findings-and-Challenges)
 * [Observational Overfitting in Reinforcement Learning](https://shagunsodhani.com/papers-I-read/Observational-Overfitting-in-Reinforcement-Learning)
 * [Rapid Learning or Feature Reuse? Towards Understanding the Effectiveness of MAML](https://shagunsodhani.com/papers-I-read/Rapid-Learning-or-Feature-Reuse-Towards-Understanding-the-Effectiveness-of-MAML)

site/_posts/2020-02-06-Your Classifier is Secretly an Energy-Based Model, and You Should Treat it Like One.md

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+---
+layout: post
+title: Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One
+comments: True
+excerpt: 
+tags: ['2019', 'ICLR 2020', 'Adversarial Robustness', 'Energy-Based Models',  'Generative Models', 'Hybrid Models', 'Out of Distribution', 'Outlier Detection', 'Out of Distribution Detection',  AI, Adversarial, Calibration, EBM, ICLR, Robustness]
+
+---
+
+## Introduction
+
+* The paper proposed a framework for joint modeling of labels and data by interpreting a discriminative classifier *p(y\|x)* as an energy-based model *p(x, y)*.
+
+* Joint modeling provides benefits like improved calibration (i.e., the predictive confidence should align with the miss classification rate), robustness, and out of order distribution.
+
+* [Link to the paper](https://arxiv.org/abs/1912.03263)
+
+## Motivation
+
+* Consider a standard classifier $f_{\theta}(x)$ which produces a k-dimensional vector of logits.
+
+* $p_{\theta}(y \| x) = softmax(f_{\theta}(x)[y])$
+
+* Uisng concepts from energy based models, we write $p_{\theta}(x, y) = \frac{exp(-E_{\theta}(x, y))}{Z_{\theta}}$ where $E_{\theta}(x, y) = -f_{\theta}(x)[y]$
+
+* $p_{\theta}(x) = \sum_{y}{ \frac{exp(-E_{\theta}(x, y))}{Z_{\theta}}}$
+
+* $E_{\theta}(x) = -LogSumExp_y(f_{\theta}(x)[y])$
+
+* Note that in the standard discriminative setup, shiting the logits $f_{\theta}(x)$ does not affect the model but it affects $p_{\theta}(x)$.
+
+* Computing $p_{\theta}(y \| x)$ using $p_{\theta}(x, y)$ and $p_{\theta}(x)$ gives back the same softmax parameterization as before.
+
+* This reinterpreted classifier is referred to as a Joint Energy-based Model (JEM).
+
+## Optimization
+
+* The log-liklihood of the data can be factoized as $log p_{\theta}(x, y) = log p_{\theta}(x) + log p_{\theta}(y \| x)$.
+
+* The second factor can be trained using the standard CE loss. In contrast, the first factor can be trained using a sampler based on Stochastic Gradient Langevin Dynamics.
+
+## Results
+
+### Hybrid Modelling
+
+* Datasets: CIFAR10, CIFAR100, SVHN.
+
+* Metrics: Inception Score, Frechet Inception Distance
+
+* JEM outperforms generative, discriminative, and hybrid models on both generative and discriminative tasks.
+
+### Calibration
+
+* A calibrated classifier is the one where the predictive confidence aligns with the misclassification rate.
+
+* Dataset: CIFAR100
+
+* JEM improves calibration while retaining high accuracy.
+
+### Out of Distribution (OOD) Detection
+
+* One way to detect OOD samples is to learn a density model that assigns a higher likelihood to in-distribution examples and lower likelihood to out of distribution examples.
+
+* JEM consistently assigns a higher likelihood to in-distribution examples.
+
+* The paper also proposes an alternate metric called *approximate mass* to detect OOD examples.
+
+* The intuition is that a point could have likelihood but be impossible to sample because its surroundings have a very low density.
+
+* On the other hand, the in-distribution data points would lie in a region of high probability mass.
+
+* Hence the norm of the gradient of log density could provide a useful signal to detect OOD examples.
+
+### Robustness
+
+* JEM is more robust to adversarial attacks as compared to discriminative classifiers.