in 📓 Notes

# Machine Learning Engineering

These are notes for the 2AMM15 course at TU/e. This content is based on the course material, and thus, may be copyrighted.

## Introduction

### What is ML?

• Learn to perform a task, based on experience (examples) $X$, minimizing error $\mathcal{E}$. E.g. recognize a flower in an image as accurately as possible
• Learn a model $f$ with some parameters $\theta$ that produces the right output $y$
• Part of a much larger system that provides the data $X$ in the right format

$$f_{\theta}(X) = y$$ $$\underset{\theta}{\operatorname{argmin}} \mathcal{E}(f_{\theta}(X))$$

### Inductive bias

• We put assumptions into the model: inductive bias $b$.
• What should the model look like?
• Mimick human brain: Neural Networks
• Logical combination of inputs: Decision Trees, Linear Models
• Remember similar examples: Nearest Neighbors, SVMs
• Probability distribution: Bayesian models
• Hyper parameters: user defined settings. E.g. depth of tree, network architecture.
• Assumptions about the data distribution. E.g. $X \sim N(\mu,\sigma)$.
• We can transfer knowledge from previous tasks: $f_1, f_2, f_3, … \Longrightarrow f_{new}$.
• Choose the right model, hyper parameters
• Reuse previously learned values for model parameters $\theta$
• In short: $\underset{\theta,b}{\operatorname{argmin}} \mathcal{E}(f_{\theta, b}(X))$

### Machine Learning vs Statistics

• Both:
• Predictions of natural phenomena
• Statistics
• Help humans understand the world
• Assume data is generated according to an understandable model
• Machine learning
• Assume data generation process is unknown
• Engineering-oriented, less mathematical theory

### Types of Machine Learning

• Many times, we combine more than one type

Supervised Machine Learning

• Learn a model $f$ from labeled data $(X, y)$, i.e., from ground truth
• Supervised: we know the correct/desired outcome (label)
• Classification
• Predict a class label (category), discrete and unordered
• Can be binary (e.g. spam/not spam) or multi-class (e.g. letter recognition)
• Many classifiers can return a confidence per class
• The predictions of the model yield a decision boundary separating the classes
• Regression
• Predict a continuous, numeric value. E.g. temperature.
• Target variable is numeric
• Some algorithms can return a confidence interval
• Find relationship between predictors and the target

Semi-Supervised Learning

• Learn a model rom few labeled and many unlabeled examples
• Unlabeled examples add information about which new examples are likely to occur

Unsupervised Machine Learning

• Explore the structure of the data $X$ to extract meaningful information
• Given inputs $X$, find which ones are special, similar, anomalous, etc
• Unlabeled data, or data with unknown structure
• There exist many subtypes
• Clustering
• Organize information into meaningful subgroups (clusters)
• Objects in cluster share certain degree of similarity and dissimilarity to other clusters
• E.g. distinguish different types of customers
• Dimensionality reduction
• Data can be very high-dimensional and difficult to understand, learn from, store, etc
• Can compress the data into fewer dimensions, while retaining most of the information
• Contrary to feature selection, the new features lose their original meaning
• The new representation can bne a lot easier to model and visualize

Reinforcement Learning

• Develop an agent that improves its performance based on interactions with the environment. E.g. Chess, Go, etc
• Search a large space of actions and states
• Reward function defines how well a series of actions works
• Learn a series of actions (policy) that maximizes reward through exploration

### Learning = Representation + Evaluation + Optimization

ML algorithms consist of 3 components:

• Representation: a model $f_{\theta}$ must be represented in a formal language that the computer can handle
• Defines the “concepts” it can learn, the hypothesis space
• E.g. a decision tree, neural network, set of annotated data points
• Evaluation: an internal way to choose one hypothesis over the other
• Objective function, scoring function, loss function $\mathcal{L}(f_{\theta})$
• E.g. difference between correct output and predictions
• Optimization: an efficient way to search the hypothesis space
• Start from simple hypothesis, extend (relax) if it doesn’t fit the data
• Many methods, differing in speed of learning, number of optima, etc

Example (neural networks)

• Representation: 2 model parameter ($\theta_0,\theta_1$)
• Evaluation: a loss function $\mathcal{L}(f_{\theta})$ computes how good the predictions are
• Estimated on a set of training data with the correct predictions
• We can’t see the full surface, only evaluate specific sets of parameters
• Optimization: find the optimal set of parameters
• Usually a type of search in the hypothesis space
• E.g. gradient descent: $\theta_i^{new} = \theta_i + \frac{\mathcal{L}(f_{\theta})}{\partial \theta_i}$

### Overfitting and underfitting

• Easy to create a model that is 100% accurate on training data, but very bad on new data
• Overfitting: building a model that is too complex for the amount of data we have
• Model peculiarities in training data (noise, biases, etc)
• Solve by making model simpler (regularization), or getting more data
• Most algorithms have hyper parameters that allow regularization
• Underfitting: building a model that is too simple given the complexity of the data
• Use a more complex model
• There are techniques to detect overfitting (e.g. bias-variance analysis)
• Build ensembles of many models to overcome both underfitting and overfitting

### Model Selection

• Next to the internal loss function, we need an external evaluation function
• Feedback signal: are we actually learning the right thing? Are we under/overfitting?
• Carefully choose to fit the application
• Needed to select between models (and hyper parameters settings)
• Data needs to be split into training and test sets
• Optimize model parameters on the training set
• Evaluate on independent test set
• Avoid data leakage:
• Never optimize hyper parameters settings on test data
• Never choose preprocessing techniques based on the test data
• To optimize hyper parameters and preprocessing as well, set aside part of training set as a validation set: keep it hidden during all training
• Do not evaluate final models on training data, except for:
• Tracking whether the optimizer converges (learning curves)
• Diagnosing under/overfitting:
• Underfitting: low training and test score
• Overfitting: high training score, low test score
• On small datasets, use multiple train-test splits to avoid sampling bias. E.g. use cross validation

### Better Models

• Algorithms need to correctly transform the inputs to the right outputs
• A lot depends on how we present the data to the algorithm
• Transform data to better representation (aka encoding or embedding)
• Can be done E2E (e.g. deep learning) or by first preprocessing the data (e.g. feature selection/generation)

### Feature Engineering

• Most machine learning techniques require humans to build a good representation of the data
• Especially when data is naturally structured. E.g. table with meaningful columns
• Feature selection, dimensionality reduction, scaling, etc
• Applied machine learning is basically feature engineering
• Nothing beats domain knowledge (when available) to get a good representation

Learning Data Transformations E2E

• It’s hard to extract good features for unstructured data. E.g. images, text
• Deep learning: learn your own representation (embedding) of the data
• Through multiple layers of representation (e.g. layers of neurons)
• Each layer transforms the data a bit, based on what reduces the error

Curse of Dimensionality

• Adding lots of features and letting the model figure it out does not work
• Our assumptions (inductive biases) often fail in high dimensions:
• Randomly shaped points in an n-dimensional space. E.g. a unit hypercube
• Almost all points become outliers at the edge of the space
• Distances between any two points will become almost identical
• Consequences
• For every dimension (feature) you add, you need exponentially more data to avoid sparseness
• Affects any algorithm that is based on distances. E.g. kNN, SVM, kernel-based methods, tree-based methods, etc
• Blessing of non-uniformity: on many applications, the data lives in a very small subspace
• We can drastically improve performance by selecting features or using lower-dimensional data representations

### More data can beat a cleverer algorithm

• More data reduces the change of overfitting
• Less sparse data reduces the curse of dimensionality
• Non-parametric models: number of model parameters grows with amount of data
• Tree-based techniques, kNN, SVM, etc
• they can learn any model given sufficient data but can get stuck in local minimums
• Parametric (fixed size) models: fixed number of parameters
• Linear models, neural networks, etc
• Can be given a huge number of parameters to benefit from more data
• Deep learning models can have millions of weights, learn almost any function
• The bottleneck is moving from data to compute/scalability

### Building ML systems

1. Preprocessing: raw data is rarely ideal for learning
• Feature scaling: bring values in same range
• Encoding: make categorical features numeric
• Discretization: make numerical features categorical
• Label imbalance correction. E.g. downsampling
• Feature selection: remove uninteresting/correlated features
• Dimensionality reduction can also make data easier to learn
• Using pre-learned embeddings. E.g. word to vector, image to vector
2. Learning and evaluating data in training, validation and test sets
3. Prediction
• Final optimized model can be used for prediction
• Expected performance is performance measured on independent test set
• Together they form a workflow or pipeline
• There exist ML methods to automatically build and tune these pipelines
• Need to optimize pipelines continuously
• Concept drift: the phenomenon you are modelling can change over time
• Feedback: models' predictions may change future data

## k-Nearest Neighbor

• Make a prediction: find the $k$ closest data points in the training dataset
• Classification: predict the most frequent class of the $k$ neighbors
• Regression: predict the average of the values of the $k$ neighbors
• Both can be weighted by the distance to each neighbor
• Main hyper parameters:
• Number of neighbors $k$, regularizer
• Choice of distance function: Euclidean, etc
• Weighting scheme: uniform, distance, etc
• Model:
• Representation: store training examples. E.g. in kd-tree
• Typical loss functions:
• Classification: accuracy (zero-one loss)
• Regression: root mean squared error
• Optimization: none (no model parameters to tune)

### Classification

• $k=1$: look at the nearest neighbor only. Likely to overfit
• $k>1$: do a vote and return the majority or confidence value for each class
• Using
• Few neighbors => high model complexity, complicated decision boundary
• Many neighbors => low model complexity, smoother decision boundary
• Nearest Shrunken Centroid
• Alternative to kNN neighbor
• Nearest centroid: represents each class by the centroid of its members
• Parametric model, while kNN is non-parametric
• Regularization is possible with the shrink threshold parameter
• Shrinks (scales) each feature value by within class variance of that feature
• Soft thresholding: if feature value falls below threshold, it is set to 0
• Effectively removes noisy features
• Suffers when data is not “convex”

Scalability

• With n = nr examples and p = nr features
• Nearest shrunken threshold
• Fit: $O(n * p)$
• Memory: $O(nrclasses * p)$
• Predict: $O(nrclasses * p)$
• Nearest neighbors (naive)
• Fit: $0$
• Memory: $O(n * p)$
• Predict: $O(n * p)$
• Nearest neighbors (with KD trees)
• Fit: $O(p * n log n)$
• Memory: $O(n * p)$
• Predict: $O(k * log n)$

### Regression

• $k=1$: return the target value of the nearest neighbor. Likely to overfit
• $k>1$: returns the mean of the target value of the $k$ nearest neighbors
• Small $k$ leads to overly complex (overfitting) model
• Larger $k$ tens to yield a smoother fit

### Pros and Cons

• Easy to understand and works well in many settings
• Training is very fast, but predicting is slow for large datasets
• Bad at high-dimensional and sparse data (Curse of Dimensionality)
• Nearest centroid is a useful parametric alternative, but only if data is near linearly separable

## Linear Models

• Predictions using a linear function of the input $X$: $f_{\mathbf{w}}(\mathbf{x}) = \sum_{i=1}^{p} w_i \cdot x_i + w_{0}$
• Learn $w$ from $X$, given a loss function $\mathcal{L}$: $\underset{\mathbf{w}}{\operatorname{argmin}} \mathcal{L}(f_\mathbf{w}(X))$
• Many algorithms with different loss functions: Least squares, ridge, lasso, logistic regression, linear SVMs, etc
• Can be very powerful (and fast), especially for large datasets with many features
• Can be generalized to learn non-linear patterns: Generalized Linear Models
• Features can be augmented with polynomials of the original features
• Features can be transformed according to a distribution (Poisson, Tweedie, Gamma, etc)
• Some linear models (e.g. SVMs) can be kernelized to learn non-linear functions

### Regression

• Prediction formula for input features $X$:
• $w_1$…$w_n$ usually called weights or coefficients, $w_0$ the bias or intercept
• Assumes that errors are $N(0,\sigma)$

$$\hat{y} = \mathbf{w}\mathbf{x} + w_0 = \sum_{i=1}^{p} w_i \cdot x_i + w_0 = w_1 \cdot x_1 + w_2 \cdot x_2 + … + w_p \cdot x_p + w_0$$

Linear Regression (Ordinary Least Squares)

• Loss function is the sum of squared errors (SSE) between predictions $\hat{y}_i$ and true regression targets $y_i$ on the training set

$$\mathcal{L}_{SSE} = \sum_{n=1}^{N} (y_n-\hat{y}_n)^2 = \sum_{n=1}^{N} (y_n-(\mathbf{w}\mathbf{x_n} + w_0))^2$$

TODO

## Decision Trees

• Representation: assume we can represent the concept we wanna learn with a decision tree
• Repeatedly split the data based on one feature at a time.
• Oblique trees can split on combinations of features.
• Evaluation/loss: one tree is better than another tree according to some heuristic
• Classification: instances in a leaf are all of the same class (pure leafs)
• Regression: instances in a leaf have values close to each other
• Optimization: recursive, heuristic greedy search (Hunt’s algorithm)
• Make first split based heuristic
• In each branch, repeat splitting in the same way

Heuristics

• We start from a dataset of $n$ points

TODO

## Neural Networks for Text

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