Lecture Notes on Gaussian Discriminant Analysis, Naive Bayes and EM Algorithm Feng Li fli@sdu.edu.cn Shandong University, China 1 Bayes’ Theorem and Inference Bayes’ theorem is stated mathematically through parameters θ = {P(X = x | Y = y), P(Y = y)}x,y. 2 Gaussian Discriminant Analysis In Gaussian Discriminate Analysis (GDA) model, we have the following as- sumptions: • A1: Y ∼ Bernoulli(ψ): Y follows ˜y | X = ˜x) = pY |X(˜y | ˜x) = p(˜x | ˜y)p(˜y) p(˜x) where ˜y = 0, 1. 3 Gaussian Discriminant Analysis and Logistic Regression By far, we introduce two classification algorithms, Logistic Regression

Lecture 5: Gaussian Discriminant Analysis, Naive Bayes and EM Algorithm Feng Li Shandong University fli@sdu.edu.cn September 27, 2023 Feng Li (SDU) GDA, NB and EM September 27, 2023 1 / 122 Outline Outline 1 Probability Theory Review 2 A Warm-Up Case 3 Gaussian Discriminate Analysis 4 Naive Bayes 5 Expectation-Maximization (EM) Algorithm Feng Li (SDU) GDA, NB and EM September 27, 2023 2 / 122 = � −1 −1.5 � Feng Li (SDU) GDA, NB and EM September 27, 2023 41 / 122 Gaussian Discriminant Analysis (Contd.) Y ∼ Bernoulli(ψ) P(Y = 1) = ψ P(Y = 0) = 1 − ψ Probability mass function pY (y) = ψy(1

the features by hand (at least in the pre deep learning era). Techniques like Principal Components Analysis, Low-Rank Matrix Factorization, etc. are popular tools for dimensionality reduction. We will explain known as the Skipgram task. In the CBOW task, taking the sentence “the quick brown fox jumps over the lazy dog”, we can mask the word “jumps” and let the neural network predict the word it thinks fits in the regular convolutions and depthwise separable convolutions respectively. It will be followed by an analysis of their performance on key metrics. The code is below, but the entire Jupyter notebook is here

"} ) eval_data_path: str = field( default=None, metadata={"help": "Path to the evaluation data."} ) lazy_preprocess: bool = False @dataclass class TrainingArguments(transformers.TrainingArguments): cache_dir: __init__() self.tokenizer = tokenizer self.max_len = max_len rank0_print("Formatting inputs...Skip in lazy mode") self.tokenizer = tokenizer self.raw_data = raw_data self.cached_data_dict = {} def __len__(self): dataset and collator for supervised fine-tuning.""" dataset_cls = ( LazySupervisedDataset if data_args.lazy_preprocess else SupervisedDataset ) (续下页) 1.12. 有监督微调 31 Qwen (接上页) rank0_print("Loading data

skip connections Decoder Details from multi-frames Analysis 52 3 identical frames Output (identical) Details from multi-frames Analysis 53 3 consecutive frames Output (consecutive) Output Layer v.s. Baseline Analysis 54 Output (baseline) ????????????????????????→0 BW Resize Backward warping + Resize (baseline) Ablation Study: SPMC Layer v.s. Baseline Analysis 55 Output (SPMC) deconv 86 Data from GOPRO dataset Using Different Number of Scales Analysis 87 1 scale Input 2 scales 3 scales Baseline Models Analysis 88 Model SS SC w/o R RNN SR-Flat Param 2.73M 8.19M 2.73M 3.03M

which makes deep learning a very powerful tool. Deep learning algorithms are also useful for the analysis of unstructured data. Let us go through the basics of deep learning in this chapter. Artificial floatx() 'float32' Let us understand some of the significant backend functions used for data analysis in brief: get_uid() It is the identifier for the default graph. It is defined below: >>> It is used to convert positive into dense vectors of fixed size. Its main application is in text analysis. The signature of the Embedding layer function and its arguments with default value is as follows

regression, logistic re- gression, regularization, Gaussian discriminant analysis, Naive Bayes, EM algorithm, SVM, K-means, factor analysis, PCA, neural networks etc. 68 hours (4 hours/week × 17 weeks) Labs Personalized tutoring Discover new knowledge from large databases (data mining) Market basket analysis (e.g. diapers and beer) Medical information mining (e.g. migraines to calcium channel blockers to these with fewer ones, without loss of information. On simple way is to use PCA (Principal Component Analysis) Suppose that all data are in a space, we first find the direction of high- est variance of these

features and enhancements. ‣ PyTorch container image version 22.09 is based on 1.13.0a0+d0d6b1f. ‣ CUDA lazy module loading is on by default. To disable it, use unset CUDA_MODULE_LOADING or set it to EAGER. PyTorch container image version 22.08 is based on 1.13.0a0+d321be6. ‣ CUDA Module loading is set to LAZY starting with the 22.08 container. To enable the default eager loading behavior, use `export CUDA 12.0a0+8a1a93a. ‣ CUDA 11.7 introduces lazy module loading, which can save memory usage in your application. To enable it, use export CUDA_MODULE_LOADING="LAZY". Announcements ‣ NVIDIA Deep Learning

sentiments of the original and the transformed sentences are consistent. This can be used for sentiment analysis. This transformation has two main implications. First, it augments our dataset with additional examples that the agreement between the text and the original label is intact. In the context of sentiment analysis, the transformation must preserve the original sentiment of the text. For a language translation augmentations. It provides a simple 5 Maas, Andrew, et al. "Learning word vectors for sentiment analysis." Proceedings of the 49th annual meeting of the association for computational linguistics: Human

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