## Lecture 4: Regularization and Bayesian Statistics Feng Li Shandong University fli@sdu.edu.cn September 20, 2023 ## Lecture 4: Regularization and Bayesian Statistics })-y^{(i)})^{2}+\lambda\sum_{j=1}^{n}\theta_{j}^{2}\right] $$ where $ \lambda $ is the regularization parameter • As the magnitudes of the fitting parameters increase, there will be an increasing

## PyTorch ## Regularization 主讲人：龙良曲 ## Occam's Razor ■ More things should not be used than are necessary.  Underfitted ## ■ More data ## Constraint model complexity - shallow regularization ## Dropout Data argumentation ## Early Stopping Regularization ## Weight Decay $$ J\left(\theta\right)=-\frac{1}{m}\sum _1.jpg)  L1-regularization $$ J\left(\theta\right)=-\frac{1}{m}\sum_{i=1}^{m}\left[y_{i}\ln\hat{y}_{i}+\left(1-y_{i}\

主讲人：龙良曲 ## Tricks Early Stopping Dropout ■ Stochastic Gradient Descent ## Early Stopping ■ Regularization  ## How-To ☑

layer, etc., Keras model and layer access Keras modules for activation function, loss function, regularization function, etc., Using Keras model, Keras Layer, and Keras modules, any ANN algorithm (CNN, RNN optimization. Keras regularization module provides below functions to set penalties on the layer. Regularization applies per-layer basis only. ## L1 Regularizer It provides L1 based regularization. from keras regularizer represent the regularizer to be used in the layer. ## L2 Regularizer It provides L2 based regularization. from keras.models import Sequential from keras.layers import Activation, Dense from keras import

how label smoothing can help us avoid overfitting. ## Label Smoothing Label smoothing is a regularization method that helps reduce the overfitting we might see with our models where the model predicts way too noisy for the model to learn anything. You should treat label smoothing as yet another regularization technique. In fact this paper $ ^{17} $ goes into details about when label smoothing helps. optimizer should prefer a flatter minima over a steeper minima. This idea is intuitively analogous to regularization where we prefer to find solutions with model parameters having smaller absolute values due to

smaller footprints. In the first chapter, we briefly introduced learning techniques such as regularization, dropout, data augmentation, and distillation to improve quality. These techniques can boost namely data augmentation and distillation, to discuss in this chapter. This is because, firstly, regularization and dropout are fairly straightforward to enable in any modern deep learning framework. Secondly l2(params.get('l2_reg_weight', 2e-4)) # Find the dropout rate for helping with further regularization. dropout_rate = params.get('dropout_rate', 1.0) # We will keep the first 'block'

and algorithms in machine learning. The topics include linear regression, logistic regression, regularization, Gaussian discriminant analysis, Naive Bayes, EM algorithm, SVM, K-means, factor analysis, PCA have very well, but do poorly on new data (poor generalization ability). • Cross-validation, regularization, • Reducing dimensionality is another possibility. - It is apparent that things become simpler

3/0/c/c30c137bd581cbe5e35e46bb0d027e3c/p3_3.jpg) ## Limited Data Small network capacity ■ Regularization Data argumentation ## ☀️ ☁️ ☁️ cifar_train = datasets.CIFAR10('cifar', True, transform=transforms

params) • GPU implementation (50x speedup over CPU) • Trained on two GPUs for a week • Dropout regularization K. Simonyan and A. Zisserman, ## V GG ## V GGNet: ILSVRC 2014 2 $ ^{nd} $ place 3x3 1x1

声的影响。 ### 2. 降维 即丢弃一些不能帮助我们正确预测的特征。可以是手工选择保留哪些特征，或者使用一些模型选择的算法来帮忙（例如PCA）。 ### 3. 正则化 正则化(regularization)的技术，保留所有的特征，但是减少参数的大小（magnitude），它可以改善或者减少过拟合问题。 ### 4. 集成学习方法 集成学习是把多个模型集成在一起，来降低单一模型的过拟合风险。