Intro to Machine Learning

What is Machine Learning?

• Machine learning automates better predictions from past experiences.
• It is used predicting spam emails, forecasting sales, and recommending movies.
• It has relations to data mining and statistical modeling.

How Machine Learning Works

• Data collection serves to gather relevant information
• Model selection entails choosing an appropriate machine learning model.
• Model training uses the data for model training.
• Model evaluation tests on new data to gauge performance.
• Model deployment uses the model to make predictions on new data.

Common Machine Learning Tasks

• Classification assigns data to categories.
• Regression predicts a value.
• Clustering groups similar data points.
• Dimensionality reduction reduces the number of variables in the data.
• Association rule learning discovers relationships between variables.

Types of Machine Learning

• Supervised learning uses labeled data to train the model.
  • Classification and Regression.
• Unsupervised learning uses unlabeled data for model training.
  • Clustering and Dimensionality reduction.
• Reinforcement learning trains a model to make decisions in an environment to maximize reward.

Challenges of Machine Learning

• Insufficient data causes not enough data to train a good model.
• Non-representative data means data do not accurately reflect the real world.
• Poor data quality can cause incomplete, inaccurate or inconsistent data.
• Irrelevant features don't help the model make accurate predictions.
• Overfitting yields good performance on training data but poor performance on new data.
• Underfitting means the model is too simple to capture the patterns in the data.

Testing and Validating

• Training sets are data used to train models
• Test sets data used to evaluate models after training.
• Validation sets data used to tune hyperparameters during training

Hyperparameters vs Model Parameters

• Model parameters are learned during training.
• Hyperparameters are set before training.

Example of Machine Learning

• To predict house prices based on features: gather data, select a model, train, evaluate then use model to predict prices of new houses.

End-to-End Project Key Steps

• Look at the big picture defines the objective and how the model is used.
• Getting the data is gathering data for it's various sources.
• Explore the data to vizualize gain insights
• Prepare the data involves cleaning, transforming and scaling.
• Shortlisting promising models involves training and evaluating a few models.
• Fine-tuning the system optimizes models and hyperparameters.
• Presenting the solution communicates findings and recommendations.
• Launch, monitor, and maintain the model and monitor its performance.

Data Handling

• Fresh data is regularly fetched using an automated download process.
• Data is understood using the data structure like CSV, SQL or JSON.
• The data quick look into data is available in head(), info(), and describe() methods in Pandas.

Data Exploration

• Histogram and scatter plots give the ability to vizualize data
• Correlations between features show correlation does not imply causation.
• Combining existing ones create new features by Attributes Combinations

Data Preparation

1. Data Cleaning is handling missing values, outliers etc.
2. Encoding Text and Categorical Attributes will convert text and categorical data into numerical data.
3. Feature Scaling is used to scale the features to a similar range.
4. Transformation Pipeline automates data preparation steps.

Select and Train

1. Training and Evaluating is used to train different models and evaluate its performance
2. Cross-Validation is splitting the training in to multiple subsets to evaluate the model more robustly.

Fine Tune

1. Grid Search can systematically search for the best hyperparameter values.

2. Randomized Search: Randomly sample hyperparameter values.

3. Ensemble Methods: Combine multiple models to improve performance.

Solution Presentation

1. Document everything by keeping a detailed record of all steps taken.
2. The visual communication is compelling using visuals for findings.

Launch, Monitor, and Maintain

1. Monitor performance by Regulary checking
2. Retrain Data by using new Data.

Classification Definition

• Predicting a categorical class label
• Spam detection and image recognition are examples.

Performance Measurement

• Measuring Accuracy are tools using Cross-Validation to measure.

• Confusion Matrix summarizes the performance of a classification model.

• Precision is the accuracy of positive predictions. $\text{Precision} = \frac{TP}{TP + FP}$

• Recall is the ratio of positive instances that are correctly detected.

  • $\text{Recall} = \frac{TP}{TP + FN}$

• Precision/Recall Trade-off adjusts the threshold to balance.

• ROC plots the true positive rate (recall) against the false positive rate.

Components

• True Positive (TP) is a correctly predicted positive instance.
• False Positive (FP) is an incorrectly predicted positive instance.
• False Negative (FN) is a incorrectly predicted negative instance.

Multiclass Classification

• In One-versus-all (OvA) it is using One classifier for each class.
• One-versus-one (OvO) means training a classifier for every pair of classes.

Error Analysis

• Analyze types of errors to look at identified error types.

Multilabel & Multioutput Classication

Multilabel is where one classifies the samples for multiple label objects in a image. Multioutput Classication is a generalization of multilabel using multi class classifications for each label.

Linear Regression

• Equation:
  • $\hat{y} = \theta_0 + \theta_1x_1 + \theta_2x_2 +... + \theta_nx_n$
• Cost function:
  • MSE (Mean Squared Error)
    • $MSE = \frac{1}{m}\sum_{i=1}^{m}(\theta^T \cdot x^{(i)} - y^{(i)})^2$
• Normal Equation:
  • $\hat{\theta} = (x^T \cdot X)^{-1} \cdot X^T \cdot y$

Gradient descent

• Batch Gradient Descent is using all data to compute gradient
• Stochastic Gradient Descent uses one random instance at a time.
• Mini-Batch Gradient Descent uses small random sets of instances.

Polynomial

• Adding polynomial features transformation to data to fit non-linear relationships.

Learning Curves

• Graphing the model performance that visualize the performance to detect the errors

Regularized Linear Model

• Ridge Regression adds $l_2$ regularization term to the cost function. $J(\theta) = MSE(\theta) + \alpha\frac{1}{2}\sum_{i=1}^{n}\theta_i^2$
• Lasso Regression adds $l_1$ regularization term to the cost function.
  • $J(\theta) = MSE(\theta) + \alpha\sum_{i=1}^{n}|\theta_i|$
• Elastic Net is the combination for the Ridge and Lasso Regression.

  • -   $J(\theta) = MSE(\theta) + r\alpha\sum_{i=1}^{n}|\theta_i| + \frac{1-r}{2}\alpha\sum_{i=1}^{n}\theta_i^2$
    

• Early Stopping is where to Stop training when reaching the minimum.

Logistic Regression

• Estimating Probabilities:
  • $\hat{p} = h_{\theta}(x) = \sigma(\theta^T \cdot x)$
  • $\sigma(t) = \frac{1}{1 + e^{-t}}$
• Cost Function:
  • $J(\theta) = -\frac{1}{m}\sum_{i=1}^{m}[y^{(i)}log(\hat{p}^{(i)}) + (1-y^{(i)})log(1 - \hat{p}^{(i)})]$

Softmax Regression

• Softmax Score:
  • $s_k(x) = (\theta^{(k)})^T \cdot x$
• Softmax Function:
  • $\hat{p}_k = \sigma(s(x))k = \frac{e^{s_k(x)}}{\sum{j=1}^{K}e^{s_j(x)}}$
• Cross-Entropy Cost Function:
  • $J(\Theta) = -\frac{1}{m}\sum_{i=1}^{m}\sum_{k=1}^{K}y_k^{(i)}log(\hat{p}_k^{(i)})$ # Lecture 5: October 2, 2023

Star Formation History

• The rate of star birth described as a function of time

• Equation:

• $\psi(t) = \frac{dM_*}{dt}$ [M$_\odot$ /yr]

• A single age stellar population that is exponentially declining is defined as Burst:

  • $\psi(t) = \psi_0 e^{-t/\tau}$

• Simple Stellar Population (SSP) that are coeval with that of the same metallicity.

Spectral Synthesis

• Combine SSPs of different ages & metallicities to reproduce the observed spectrum of a galaxy. The weights are determined by the star formation history.
• $M/L_*$ ratio is massive Stars that contributes to light, but low mass stars dominate mass budget.

IMF (Initial Mass Function)

• Distribution stars mass based at birth.
• $\frac{dN}{dM} \propto M^{-\alpha}$
• Relatively few massive stars with a few solar masses.

Metallicity

• Is a mass fraction
• $Z = \frac{M_Z}{M_{gas}}$ (mass fraction)
• Logarithmic scale: $[Fe/H] = log_{10} \frac{(Fe/H){star}}{(Fe/H){\odot}}$
• Solar: $Z_\odot \approx 0.014$

Dust

• Dust absorbs and scatters light for dust extinction
• grains are created in the wings of AGB stars & supernova.

Nebular Emission

• HII regions uses gas ionized using young hot stars
• Lines ratios determines physical conditions.

Regla de la Potencia

• $\int x^n dx = \frac{x^{n+1}}{n+1} + C$, $n \neq -1$

Exponenciales

• $\int e^x dx = e^x + C$
• $\int a^x dx = \frac{a^x}{\ln(a)} + C$, $a>0$, $a \neq 1$

Funciones Trigonométricas

• $\int \sin(x) dx = -\cos(x) + C$
• $\int \cos(x) dx = \sin(x) + C$
• $\int \sec^2(x) dx = \tan(x) + C$
• $\int \csc^2(x) dx = -\cot(x) + C$
• $\int \sec(x)\tan(x) dx = \sec(x) + C$
• $\int \csc(x)\cot(x) dx = -\csc(x) + C$

Funciones Racionales

• $\int \frac{1}{x} dx = \ln|x| + C$

Funciones Trigonométricas Inversas

• $\int \frac{1}{\sqrt{1-x^2}} dx = \sin^{-1}(x) + C$
• $\int \frac{1}{1+x^2} dx = \tan^{-1}(x) + C$
• $\int \frac{1}{x\sqrt{x^2-1}} dx = \sec^{-1}(x) + C$

General Instructions

• Use a pen with black or dark blue ink to darken the ovals completely.
• Mark only one oval for each question. If you change your answer, be sure to erase completely.
• Answer all questions. Only responses marked on your answer sheet will be scored.
• Responses written in the free-response booklets will not be scored.

Important Reminders

• A CALCULATOR MAY BE USED ON PARTS A OF QUESTIONS 1 AND 2 AND ON QUESTIONS 3 AND 4.
• A calculator is not allowed on parts B of questions 1 and 2 and on questions 5 and 6.

Installation and function of Matplotlib

• matplotlib is a comprehensive library for creating static, animated, and interactive visualizations in Python.
• Pip Installation usage:

pip install matplotlib

Pyplot function with matplotlib

• matplotlib.pyplot is a collection of functions that make Matplotlib work like MATLAB.
• Each pyplot function makes some change to a figure: e.g., creates a figure, creates a plotting area in a figure, plots some lines in a plotting area, decorates the plot with labels, etc.

Figures for Plotting

• can have multiple plots the whole page is the figure to showcase

Axes for multiple plotting

• Plots are also called axes in Matplotlib. So, a figure can have multiple axes.
• Every plotting function takes numpy.ndarray as input.

Working with text function

• It uses different text for formatting different labels

Annotation function

• uses arrows and annotaions to use as a guide

Consejos para detectar noticias falsas

• Los medios de comunicación son un conducto peligroso de mentiras que imitan la calidad de los bienes y servicios

¿Cómo detectar las noticias falsas?

• Evalua al fuente.
• Evalúa al contenido.
• Examinar fuentes y titulos.
• Comprobar al autor preguntando a uno de los expertos en el tema
• Consultar expertos.

Medidas de Dispersión

• el rango o la amplitud total es la diferencia entre la observación mayor y la observación menor.
• El rango intercuartílico (RIC) es la diferencia entre el tercer cuartil ($Q_3$) y el primer cuartil ($Q_1$).
• la varianza poblacional es una medida de la variabilidad de un conjunto de datos con respecto a su media

Cost Accounting and Capital Cost Estimation

General Accounting Principles

• Accounting is the method of collecting, summarizing, and reporting financial information. Accounting Terms
• Assets: anything of value owned by the company
• Assets = Liabilities + Owner’s Equity
• Revenue: the increase in owner’s equity due to the sale of goods or services
• Expenses: the decrease in owner’s equity due to using resources to produce revenue

Financial Statements

Income Statement: indicates the profitability of a company during a period of time Net Income = Revenues - Expenses Balance Sheet: indicates what a company owns and owes at a specific point in time Assets = Liabilities + Owner’s Equity Statement of Cash Flows: indicates the movement of cash both into and out of a company during a period of time