1. Deild Promotion Playoff stats & predictions

A Deep Dive into Match Statistics: What Numbers Say About Tomorrow’s Games?

• Possession Percentages: ntrrguo/ntrrguo.github.io<|file_sep|>/_posts/2019-12-18-Summary-of-Machine-Learning-Research.md --- layout: post title: Summary of Machine Learning Research date: 2019-12-18 categories: blog tags: [Machine Learning] description: I will summarize some interesting research work I have read recently. --- I will summarize some interesting research work I have read recently. ## Graph Neural Networks [Neural Message Passing for Quantum Chemistry](https://arxiv.org/pdf/1704.01212.pdf) ### Problem This paper uses graph neural networks (GNN) to predict quantum properties of molecules. ### Solution The paper proposes a novel message passing scheme between nodes in graphs which describes molecular structure.  The idea is that we iteratively update node embeddings by sending messages from neighboring nodes using differentiable functions. $$ v_i^{(t+1)} = text{UPDATE}^{(t)}left(v_i^{(t)}, text{AGGREGATE}^{(t)}left(left{ text{MESSAGE}^{(t)}left(v_i^{(t)}, v_j^{(t)}, e_{ij}right) | j in mathcal{N}(i) right}right)right) $$ ### Result  The paper achieves state-of-the-art results compared with traditional quantum chemistry models. ### Extension [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://arxiv.org/pdf/1704.02901.pdf) This paper improves message passing scheme by using edge information when aggregating messages from neighbors. ## Adversarial Machine Learning [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://arxiv.org/pdf/1806.00069.pdf) ### Problem This paper discusses interpretability issue when applying machine learning models. ### Solution The paper reviews several methods including decision trees (interpretable but less accurate), LIME (less accurate but interpretable), rule lists (interpretable but less accurate), attention models (accurate but not interpretable), etc. ### Result The paper compares different methods using human study:  ## Adversarial Attacks [Adversarial Examples Improve Image Recognition](https://arxiv.org/pdf/1712.02779.pdf) ### Problem This paper investigates whether adversarial examples can improve model accuracy. ### Solution The paper proposes using adversarial examples during training as extra data points.  ### Result The paper shows that adversarial examples do help improve model accuracy:  ## Reinforcement Learning [Learning Deep Structured Semantic Models for Web Search Using Clickthrough Data](https://arxiv.org/pdf/1506.00999.pdf) ### Problem This paper investigates whether reinforcement learning can help improve web search ranking. ### Solution The paper uses reinforcement learning algorithm DQN:  DQN takes page features as input $x_t$, outputs page scores $a_t$ as action $a_t = f(x_t)$ where $f$ is deep neural network function approximator. Page scores $a_t$ is used as ranking policy $pi(a_t|x_t)$. Rewards $r_t$ is click-through rate (CTR) data given current ranking policy. Value function $Q(s,a)$ represents how good action $a$ taken at state $s$ will be. Q-value $Q(s,a)$ can be updated using Q-learning algorithm: $$ Q(s,a) gets Q(s,a) + alpha cdot [r + gamma cdot max_a Q(s',a) - Q(s,a)] $$ where $alpha$ is learning rate and $gamma$ is discount factor. DQN uses replay memory which stores transitions $(s,a,r,s')$ so that transitions are sampled randomly when updating Q-values. Deep neural network function approximator $f$ estimates Q-values $Q(s,a)$ given state-action pair $(s,a)$. Target network $hat{f}$ is used as fixed Q-value function approximator when updating Q-values so that changes in estimated Q-values don't affect target values used when updating Q-values. Target network $hat{f}$'s parameters $theta_{hat{f}}$ are updated slowly from main network $f$'s parameters $theta_f$: $$ theta_{hat{f}} leftarrow tau cdot theta_f + (1 - tau) cdot theta_{hat{f}} $$ where $tau$ controls how fast target network parameters change from main network parameters. ### Result  The paper shows that DQN outperforms traditional ranking algorithms such as RankSVM. ## Generative Adversarial Networks [Improved Techniques for Training GANs](https://arxiv.org/pdf/1606.03498.pdf) ### Problem This paper investigates ways to stabilize GAN training. ### Solution The paper proposes three techniques: 1) Replace weight clipping with weight normalization using gradient penalty term: $$ L = L_{GAN} + lambda (|nabla_{hat{x}} D(hat{x})|_2 - 1)^2 $$ where $lambda$ controls how important gradient penalty term is. $nabla_{hat{x}} D(hat{x})$ represents gradient of discriminator output w.r.t input image. $|cdot|_2$ represents L2 norm. $hat{x}$ represents interpolated image between real image and generated image: $$ hat{x} = z_{real} + t(z_{fake} - z_{real}) $$ where $z_{real}$ represents real image vector. $t$ represents random number sampled uniformly from range [0,1]. 2) Use batch normalization instead of layer normalization. Batch normalization normalizes data along batch dimension while layer normalization normalizes data along channel dimension. Batch normalization introduces noise which helps stabilize GAN training. Layer normalization doesn't introduce noise which makes GAN training unstable. However batch normalization has following problems: * Not compatible with recurrent neural networks because it uses mean/variance statistics over batch dimension while recurrent neural networks use temporal statistics over time dimension. * Not compatible with conditional GAN because it requires same statistics across all classes which introduces unwanted correlations across classes. To address these problems this paper proposes spectral normalization which normalizes weight matrices instead of normalizing activations like batch normalization does. Spectral normalization normalizes weight matrices along singular value dimension so it doesn't depend on batch size like batch normalization does so it doesn't introduce noise like batch normalization does so it doesn't have problems mentioned above like batch normalization does while still stabilizing GAN training like batch normalization does. Spectral norm $sigma(W)$ of matrix $W$ represents largest singular value: $$ sigma(W) = max_{x:|x|=1} |Wx| $$ Spectral normalized matrix $hat{W}$ is defined as follows: $$ hat{W} = W/sigma(W) $$ To compute spectral norm efficiently power iteration method is used: python def power_iteration(W): u = tf.random_normal([W.shape[0]]) v = tf.matmul(W,u) v /= tf.norm(v) u = tf.matmul(tf.transpose(W),v) u /= tf.norm(u) return u,v To compute spectral normalized matrix efficiently only one power iteration step needs to be done before every forward pass through discriminator: python def spectral_norm(W): u,v = power_iteration(W) sigma = tf.matmul(tf.matmul(tf.transpose(u),W),v) return W/sigma Then discriminator weights need to be updated as follows: python W.assign(spectral_norm(W)) This ensures that weights remain normalized after every forward pass through discriminator. 3) Use mini-batch discrimination which adds extra features computed across whole mini-batch instead of just single example: * For each example compute feature vector $x_i$ * For each example compute distance vector $d_i = |x_i - x_j|$ where $j=1...B$ * Concatenate distance vectors together into matrix $D$ * Apply fully connected layer with ReLU activation function on matrix D resulting in new feature matrix E * Concatenate original feature vectors x with new feature vectors e resulting in final feature matrix F * Pass final feature matrix F through rest of discriminator layers as usual ### Result  The paper shows that proposed techniques improve GAN training stability compared with original Wasserstein GAN.<|file_sep|># ntrrguo.github.io<|file_sep|># ntrrguo.github.io ## Install Install dependencies: bash bundle install Run local server: bash bundle exec jekyll serve <|repo_name|>ntrrguo