following rules hold: • Direct sum: K(x, z) = K1(x, z) + K2(x, z) • Scalar product: K(x, z) = αK1(x, z) • Direct product: K(x, z) = K1(x, z)K2(x, z) Kernels can be constructed by composing these rules. In In SVM, Mercer’s condition can be translated to another way to check whether K is a valid kernel. The kernel function K also defines the so-called ker- nel matrix over the data set (also denoted by K).

for ∀j ∈ [n]) in the above discussion. What if Xj ∈ {1, 2, · · · , v}? Can we get similar results? Check it by yourselves! 4.4 Laplace Smoothing Consider the following special case, in the give finite given that its label is j follows a Gaussian distribution parametrized by µj and Σj According to the rules of the EM algorithm, we have repeat the following steps until convergence • (E-step) For each i,

September 6, 2023 17 / 57 Example 1: Handwritten Digit Recognition Handcrafted rules will result in large number of rules and exceptions Better to have a machine that learns from a large training set

链式法则 主讲人：龙良曲 Derivative Rules Basic Rule ▪ ? + ? ▪ ? − ? Product rule ▪ ?? ′ = ?′? + ??′ ▪ ?4′ = ?2 ∗ ?2 ′ = 2? ∗ ?2 + ?2 ∗ 2? = 4?3 Quotient Rule ▪ ? ? = ?′?+??′ ?2 ▪ e.g. Softmax Chain

/backprop_old.pdf NO! Multi-Layer Perceptron is coming ▪ New Issue: How to train MLP ▪ Chain Rules => Backpropagation http://www.iro.umontreal.ca/~vincentp/ift3395/lectures/backprop_old.pdf Backpropagation:

如何将教室里的学生按爱好、身高划分为5类？ ✓ 降维（ Dimensionality Reduction ） ✓ 如何将将原高维空间中的数据点映射到低维度的空间中？ ✓ 关联规则（ Association Rules） ✓ 很多买尿布的男顾客，同时买了啤酒，可以从中找出什么规律来提 高超市销售额？ ✓ 推荐系统（ Recommender systems） ✓ 很多客户经常上网购物，根据他们的浏览商品的习惯，给他们推荐

z) Direct product: K(x, z) = K1(x, z)K2(x, z) Kernels can also be constructed by composing these rules Feng Li (SDU) SVM December 28, 2021 50 / 82 The Kernel Matrix For K to be a kernel function The

3 1.关联规则概述 01 关联规则概述 02 Apriori 算法 03 FP-Growth算法 4 1.关联规则概述 关联规则 关联规则（Association Rules）反映一个事物与其他事物之间的相互依存 性和关联性。如果两个或者多个事物之间存在一定的关联关系，那么，其中 一个事物就能够通过其他事物预测到。 关联规则可以看作是一种IF-THEN关系。假设

handwritten samples in multiple inputs. Suppose, we have confusion in one input then we need to check again other inputs to recognize the correct context which takes the decision from the past. Workflow used to evaluate the prediction of the algorithm / Model (once the machine learn) and to cross check the efficiency of the learning process.  Compile the model: Compile the algorithm / model, the prediction with actual result of the test data.  Freeze, Modify or choose new algorithm: Check whether the evaluation of the model is successful. If yes, save the algorithm for future prediction

vsphere, kubernetes pip install "skypilot-nightly[aws,gcp]" 随后，您需要用如下命令确认是否能使用云： sky check For more information, check the official document and see if you have set up your cloud accounts correctly. Alternatively transformers.Trainer, output_dir: str, bias="none" ): """Collects the state dict and dump to disk.""" # check if zero3 mode enabled if deepspeed.is_deepspeed_zero3_enabled(): state_dict = trainer.model_wrapped issue that there␣ �→are problems with # loading the checkpoint when using LoRA with DeepSpeed. # Check this issue https://github.com/huggingface/peft/issues/746 for more␣ �→information. if ( list(pathlib