machine learning fundamentals

ml

trad programs: define algo/logic to compute output

ml: learn model/logic from data

ml = study of also that: improve their performance P at some task T with experience E 

• well defined learning task = given by <P, T, E>

why use ML? + applications

-human expertise doesn’t exist (navigating Mars)

-humans x explain their expertise (speech recognition )

-models must be customised (personalised medicine)

-models = based on huge amts of data (genomics)

applications:

recognising patterns

generating patterns

recognising anomalies

prediction

data sets + features

data set

= set of data grouped into a collection with which developers can work to meet their goals. In a dataset, rows represent the no of data points + column = features of data set

features of dataset = most critical aspect- based on the features of each available data point, is there any possibility of deploying models to find output to predict the features of any nee data point that may b added to data set

data

feature scaling

= scale data to a fixed range [0,1]

• normalisation = rescale data x using the mean 𝜇 + the s.d. 𝜎 of the data

= (x- 𝜇) / 𝜎

• min max scaling: (x - x_min) / (x_max - x_min)

types of data:

numerical (quantitive): continuous, discrete

categorical (qualitative): ordinal, nominal

the task T

tasks = usually described in terms of how the machine learning should process and example: 𝑥 ∈ R^𝑛 where each entry x_i = a feature

classification: learn f: Rⁿ → {1,…,k}

• y=f(x): assigns input to the category with output y

• example: object recognition

regression: learn f: Rⁿ → R

• example: weather prediction, real estate price prediction

the experience E

supervised learning:

• experience is a labelled dataset (or datapoints)

• each data point has a label or target

unsupervised learning:

• experience = unlabelled data set

• clustering, learning probability distribution, demonising etc.

reinforcement learning:

• experience is the interaction with an environment

types of learning

supervised learning

given (x₁, y₁), (x₂, y₂), … (x_n, y_n)

learn a function f(x) to predict y given x

• y is real-valued == regression

• y is categorical == classification

the performance measure P

accuracy = proportion of examples for which the model produces the correct output

error rate: proportion of examples for which the model produces an incorrect output

loss function: quantifies the difference between the predicted outputs of a ml also + the actual target vals

generalisation: ability to perform well on previously unobserved data e.g. evaluate performance using test set

learning process

X = input space, Y = output space

• given samples {(x,y)}ⁿ₁, and a loss function L

• find a hypothesis h ∈ 𝐻 that minimises ∑_{𝑖=1,...𝑛} 𝐿(h(𝒙_𝑖), 𝑦_𝑖).

0-1 loss: 𝐿(h(𝒙), 𝑦) = 1, h(x) ≠ 𝑦,otherwise 𝐿(h(𝒙),𝑦) =0

L₂ loss: 𝐿(h(𝒙), 𝑦) = (h(x) - y)²

hinge loss: 𝐿(h(𝒙), 𝑦) = max{0, 1 - yh (x)}

exponential loss: 𝐿(h(𝒙), 𝑦) = e ^-yh(x)

no free lunch theorem

argues that, w.o. having substantive info abt modelling problem, x single model that’ll always do better than any other model

goal of mlresearch isn’t to seek a universal learning algorithm or the absolute best learning algorithm 

the theorem underscores that every algorithm relies on certain assumptions abt data + success of algorithm depends on how well these assumptions align w true nature of the problem

since x also is universally superior = crucial to eval = compare diff algorithms on the specific dataset at hand

splitting the data set

training set = subset of data used to train a machine learning model

test set= the subset of data used to evaluate the performance of a trained ml model on unseen examples, simulating real-world data

validation set= intermediary subset of data used during the model development process to fine-tune hyper parameters

independent + identically distributed assumptions:

• examples in each data set = independent from each other

• training + testing set = identically distributed i.e. drawn from the same prob distribution as eachother

underfitting + overfitting

underfitting occurs when model = too simple to capture underlying patterns in the training data = poor performance on both training + test sets

• model isn’t complex enough to learn the relationships within the data

overfitting = model learns the training data too well, incl. its noise + random fluctuations leading to poor performance on new, unseen data

• model = overly complex + memorises the training set instead of learning the underlying patterns

overfitting

a hypothesis in ml is the model’s presumption regarding the connection between input features + the output 

consider hypothesis h and its

• error rate over training data: error _train(h)

• true error rate over all data: error _true(h)

hypothesis h overfits the training data is there’s an alternative hypothesis h’ that:

• error _train(h) < error _train(h’)

• error _train(h) > error _train(h’)

resolving under + overfitting

underfitting:

• ↑ model complexity

• using diff ml algorithm

• ↑ amt of training data

• ensemble methods to combine multiple models to create better outputs

• feature engineering for cresting new model features from the existing ones that may be ↑ relevant to the learning task

overfitting:

• cross validation: technique for evaluating ml models by training several ML models on subsets of the available input data + evaluating them on another subset of the data

• regularisation: technique where a penalty term = added to loss function, discouraging model from assigning too much importance to individual features

• early stopping: stopping training when a monitored metric has stopped improving

• bagging: learning multiple models in parallel + applying majority voting to choose the final candidate model

cross validation

k-fold cross validation:

• divide data into k folds

• train on k-1 folds, use the 4th fold to measure error

• repeat k times: use avg error to measure generalisation accuracy

• statistically valid + gives good accuracy estimates

leave one out cross validation (LOOCV):

• k fold cross validation with k=N, where N= no of data points

• quite accurate but expensive as need to build N models

parametric learning

parametric learning algos make strong assumptions abt form of the mapping function between the input features + output

• e.g. logistic regression, linear regression, perceptron, naive bayes, neural network

benefits of such models:

• easier to understand + interpret results

• v fast to learn from data

• don’t require as much training data

• can work well even if they do x fit data perfectly

but, by pre-emptively choosing a functional form, these methods = highly constrained to those specified form

non parametric learning

non parametric learning algos dont make assumptions about the form of the mapping function between the input features + output

• for example, SVM, k-NN, k-means, decision tree

benefits include:

• being capable of fitting a large no of functional forms

• but there are x assumptions abt the underlying function +

• can result in higher performance models for prediction

but,: requires a lot more training data, takes longer to train + prone to overfitting

classification

predictive modelling problem where a class label = predicted for a given example of input data

types of classification problems:

• binary classification

• multi-class classification

• multi-label classification

• imbalanced classification

classification applications

Medical diagnosis
oFeatures: age, gender, history, symptoms, test results. oLabel: disease.

• Email spam detection
oFeatures: sender-domain, length, images, keywords. oLabel: spam or not-spam.

• Credit card fraud detection
oFeatures: user, location, item, price. oLabel: fraud or legitimate.