COMP 875: Introductions Name, year, research area/group Why are you interested in machine learning and how does it relate to your research? What topics would you like to see covered in this course? What is Machine Learning? Using past experiences to improve future performance (on a particular task) For a machine, experiences come in the form of data
What does it mean to improve performance? Learning is guided by a quantitative objective, associated with a particular notion of loss to be minimized (or gain to be maximized) Why machine learning? Often it is too difficult to design a set of rules by hand Machine learning is about automatically extracting relevant information from data and applying it to analyze new data Source: G. Shakhnarovich
Machine Learning Steps Data collection: Start with training data for which we know the correct outcome provided by a teacher Representation: Decide how to encode the input to the learning program Modeling: Choose a hypothesis class a set of possible explanations for the data Estimation: Find best hypothesis you can in the chosen class Model selection: We may reconsider the class of hypotheses given the outcome
Each of these steps can make or break the learning outcome Source: G. Shakhnarovich Learning and Probability There are many sources of uncertainty with which learning algorithms must cope: Variability of the data Dataset collection Measurement noise Labeling errors
Probability and statistics provide an appropriate framework to deal with uncertainty Some basic statistical assumptions: Training data is sampled from the true underlying data distribution Future test data will be sampled from the same distribution Source: G. Shakhnarovich Example of a learning problem
Given: training images and their categories What are the categories of these test images? Possible representation: image of size nn pixels vector of length n2 (or 3n2 if color) Source: G. Shakhnarovich The Importance of Representation Dimensionality
Beyond vectors: complex or heterogeneous input objects Web pages Program traces Images with captions or metadata Video with sound Proteins Feature extraction and feature selection What measurements/information about the input objects are the most useful for solving the given problem? Successful representation requires domain knowledge! If we could find the ideal feature representation, we
would not even need learning! Types of learning problems Supervised Classification Regression Unsupervised Semi-supervised Reinforcement learning Active learning .
Supervised learning Given training examples of inputs and corresponding outputs, produce the correct outputs for new inputs Two main scenarios: Classification: outputs are discrete variables (category labels). Learn a decision boundary that separates one class from the other Regression: also known as curve fitting or function approximation. Learn a continuous input-output mapping from examples (possibly
noisy) Regression: example 1 Suppose we want to predict gas mileage of a car based on some characteristics: number of cylinders or doors, weight, horsepower, year etc. Source: G. Shakhnarovich Regression: example 2 Training set: faces (represented as vectors of distances
between keypoints) together with experimentally obtained attractiveness rankings Learn: function to reproduce attractiveness ranking based on training inputs and outputs Attractiveness score f(v) Vector of distances v T. Leyvand, D. Cohen-Or, G. Dror, and D. Lischinski, Data-driven enhancement of facial attractiveness, SIGGRAPH 2008
Regression: example 3 Input: scalar (attractiveness score) Output: vector-valued object (face) B. Davis and S. Lazebnik, Analysis of Human Attractiveness Using Manifold Kernel Regression, ICIP 2008 Regression: example 4 Input: scalar (age) Output: vector-valued object (3D brain image)
B. C. Davis, P. T. Fletcher, E. Bullitt and S. Joshi, "Population Shape Regression From Random Design Data", ICCV, 2007. Structured Prediction Image Word Source: B. Taskar
Structured Prediction Sentence Parse tree Source: B. Taskar Structured Prediction Sentence in two
languages Word alignment Source: B. Taskar Structured Prediction Amino-acid sequence Bond structure
Source: B. Taskar Structured Prediction Many image-based inference tasks can loosely be thought of as structured prediction Data association problem model Source: D. Ramanan
Other supervised learning scenarios Learning similarity functions from relations between multiple input objects Pairwise constraints Source: X. Sui, K. Grauman Other supervised learning scenarios Learning similarity functions from relations between
multiple input objects Triplet constraints Source: X. Sui, K. Grauman Unsupervised Learning Given only unlabeled data as input, learn some sort of structure The objective is often more vague or subjective than in supervised learning. This is more of an exploratory/
descriptive data analysis Unsupervised Learning Clustering Discover groups of similar data points Unsupervised Learning Quantization Map a continuous input to a discrete (more compact) output
2 1 3 Unsupervised Learning Dimensionality reduction, manifold learning Discover a lower-dimensional surface on which the data lives Unsupervised Learning Density estimation
Find a function that approximates the probability density of the data (i.e., value of the function is high for typical points and low for atypical points) Can be used for anomaly detection Other types of learning Semi-supervised learning: lots of data is available, but only small portion is labeled (e.g. since labeling is expensive) Other types of learning
Semi-supervised learning: lots of data is available, but only small portion is labeled (e.g. since labeling is expensive) Why is learning from labeled and unlabeled data better than learning from labeled data alone? ? Other types of learning Active learning: the learning algorithm can choose its own training examples, or ask a teacher for an
answer on selected inputs S. Vijayanarasimhan and K. Grauman, Cost-Sensitive Active Visual Category Learning, 2009 Other types of learning Reinforcement learning: an agent takes inputs from the environment, and takes actions that affect the environment. Occasionally, the agent gets a scalar reward or punishment. The goal is to learn to produce action sequences that maximize the expected reward
(e.g. driving a robot without bumping into obstacles) Apprenticeship learning: learning from demonstrations when the reward function is initially unknown Autonomous helicopter flight: Pieter Abbeel http://heli.stanford.edu/ Generalization The ultimate goal is to do as well as possible on new, unseen data (a test set), but we only have access to labels (ground truth) for the training set
What makes generalization possible? Inductive bias: set of assumptions a learner uses to predict the target value for previously unseen inputs This is the same as modeling or choosing a target hypothesis class Types of inductive bias Occams razor Similarity/continuity bias: similar inputs should have similar outputs
Achieving good generalization Consideration 1: Bias How well does your model fit the observed data? It may be a good idea to accept some fitting error, because it may be due to noise or other accidental characteristics of one particular training set Consideration 2: Variance How robust is the model to the selection of a particular training set? To put it differently, if we learn models on two
different training sets, how consistent will the models be? Bias/variance tradeoff Models with too many parameters may fit the training data well (low bias), but are sensitive to choice of training set (high variance) Bias/variance tradeoff Models with too few many
parameters parameters may may notfitfitthe the training data data (high well well (low
bias) bias), but are butconsistent are sensitive across to choice different of training sets set (high
(low variance) 2 Bias/variance tradeoff Models with too few many parameters parameters may may
notfitfitthe the training data data (high well well (low bias) bias), but are butconsistent
are sensitive across to choice different of training sets set (high (low variance) Generalization error is due to underfitting overfitting
2 Underfitting and overfitting How to recognize underfitting? High training error and high test error How to deal with underfitting? Find a more complex model How to recognize overfitting? Low training error, but high test error How to deal with overfitting? Get more training data
Decrease the number of parameters in your model Regularization: penalize certain parts of the parameter space or introduce additional constraints to deal with a potentially ill-posed problem Methodology Distinction between training and testing is crucial Correct performance on training set is just memorization! Strictly speaking, the researcher should never look at the test data when designing the system
Generalization performance should be evaluated on a hold-out or validation set Raises some troubling issues for learning benchmarks Source: R. Parr Next time The math begins Guest lecturer: Max Raginsky (Duke EE) Reading lists due to me by email by the end of next
Thursday, September 3rd A couple of sentences describing your topic A list of ~3 papers (doesnt have to be final) Date constraints/preferences If you have more than one idea, send them all (will help with conflict resolution)
