Andrew W. Moore

The following links point to a set of tutorials on many aspects of statistical data mining, including the foundations of probability, the foundations of statistical data analysis, and most of the classic machine learning and data mining algorithms.

These include classification algorithms such as decision trees, neural nets, Bayesian classifiers, Support Vector Machines and cased-based (aka non-parametric) learning. They include regression algorithms such as multivariate polynomial regression, MARS, Locally Weighted Regression, GMDH and neural nets. And they include other data mining operations such as clustering (mixture models, k-means and hierarchical), Bayesian networks and Reinforcement Learning.

I hope they're useful (and please let me know if they are, or if you have suggestions or error-corrections). Click here for a short list of topics.

**Decision Trees.**The Decision Tree is one of the most popular classification algorithms in current use in Data Mining and Machine Learning. This tutorial can be used as a self-contained introduction to the flavor and terminology of data mining without needing to review many statistical or probabilistic prerequisites. If you're new to data mining you'll enjoy it, but your eyebrows will raise at how simple it all is! After having defined the job of classification, we explain how information gain (next Andrew Tutorial) can be used to find predictive input attributes. We show how applying this procedure recursively allows us to build a decision tree to predict future events. We then look carefully at a question so fundamental, it is the basis for much of all statistics and machine learning theory: how do you choose between a complicated model that fits the data really well and an "Occam's razor" model that is succinct yet not so good at fitting data (this topic will be revisited in later Andrew Lectures, including "Cross-validation" and "VC-dimension"). We also discuss the very wide world of improvements and tweaks on the basic decision tree idea.**Information Gain.**This tutorial steps through the ideas from Information Theory that eventually lead to Information Gain...one of the most popular measures of association currently used in data mining. We visit the ideas of Entropy and Conditional Entropy along the way. Look at the lecture on Gaussians for discussion of Entropy in the case of continuous probability density functions.**Probability for Data Miners.**This tutorial reviews Probability starting right at ground level. It is, arguably, a useful investment to be completely happy with probability before venturing into advanced algorithms from data mining, machine learning or applied statistics. In addition to setting the stage for techniques to be used over and over again throughout the remaining tutorials, this tutorial introduces the notion of Density Estimation as an important operation, and then introduces Bayesian Classifiers such as the overfitting-prone Joint-Density Bayes Classifier, and the over-fitting-resistant Naive Bayes Classifier.**Probability Density Functions.**A review of a world that you've probably encountered before: real-valued random variables, probability density functions, and how to deal with multivariate (i.e. high dimensional) probability densities. Here's where you can review things like Expectations, Covariance Matrices, Independence, Marginal Distributions and Conditional Distributions. Once you're happy with this stuff you won't be a data miner, but you'll have the tools to very quickly become one.**Gaussians.**Gaussians, both the friendly univariate kind, and the slightly-reticent-but-nice-when-you-get-to-know-them multivariate kind are extremely useful in many parts of statistical data mining, including many data mining models in which the underlying data assumption is highly non-Gaussian. You need to be friend with multivariate Gaussians.**Maximum Likelihood Estimation.**MLE is a solid tool for learning parameters of a data mining model. It is a methodology which tries to do two things. First, it is a reasonably well-principled way to work out what computation you should be doing when you want to learn some kinds of model from data. Second, it is often fairly computationally tractable. In any case, the important thing is that in order to understand things like polynomial regression, neural nets, mixture models, hidden Markov models and many other things it's going to really help if you're happy with MLE.**Gaussian Bayes Classifiers.**Once you are friends with Gaussians, it it easy to use them as subcomponents of Bayesian Classifiers. This tutorial shows you how.**Cross-Validation.**Cross-validation is one of several approaches to estimating how well the model you've just learned from some training data is going to perform on future as-yet-unseen data. We'll review testset validation, leave-one-out cross validation (LOOCV) and k-fold cross-validation, and we'll discuss a wide variety of places that these techniques can be used. We'll also discuss overfitting...the terrible phenomenon that CV is supposed to present. And at the end, our hairs will stand on end as we realize that even when using CV, you can still overfit arbitrarily badly.**Neural Networks.**We begin by talking about linear regression...the ancestor of neural nets. We look at how linear regression can use simple matrix operations to learn from data. We gurgle with delight as we see why one initial assumption leads inevitably to the decision to try to minimize sum squared error. We then explore an alternative way to compute linear parameters---gradient descent. And then we exploit gradient descent to allow classifiers in addition to regressors, and finally to allow highly non-linear models---full neural nets in all their glory.**Instance-based learning (aka Case-based or Memory-based or non-parametric).**Over a century old, this form of data mining is still being used very intensively by statisticians and machine learners alike. We explore nearest neighbor learning, k-nearest-neighbor, kernel methods and locally weighted polynomial regression. Software and data for the algorithms in this tutorial are available from http://www.cs.cmu.edu/~awm/vizier. The example figures in this slide-set were created with the same software and data.**Eight Regression Algorithms.**You'll have to wait to find out Andrew's ordering on them, but based on all the foundations you've covered so far we will quickly be able to run through: Regression Trees, Cascade Correlation, Group Method Data Handling (GMDH), Multivariate Adaptive Regression Splines (MARS), Multilinear Interpolation, Radial Basis Functions, Robust Regression, Cascade Correlation + Projection Pursuit**Predicting Real-valued Outputs: An introduction to regression.**This lecture is made up entirely from material from the start of the Neural Nets lecture and a subset of the topics in the "Favorite Regression Algorithms" lecture. We talk about linear regression, and then these topics: Varying noise, Non-linear regression (very briefly), Polynomial Regression, Radial Basis Functions, Robust Regression, Regression Trees, Multilinear Interpolation and MARS.**Bayesian Networks.**The tutorial first reviews the fundamentals of probability (but to do that properly, please see the earlier Andrew lectures on Probability for Data Mining). It then discusses the use of Joint Distributions for representing and reasoning about uncertain knowledge. Having discussed the obvious drawback (the curse of dimensionality) for Joint Distributions as a general tool, we visit the world of clever tricks involving independence and conditional independence that allow us to express our uncertain knowledge much more succinctly. And then we beam with pleasure as we realize we've got most of the knowledge we need to understand and appreciate Bayesian Networks already. The remainder of the tutorial introduces the important question of how to do inference with Bayesian Networks (see also the next Andrew Lecture for that).**Inference in Bayesian Networks (by Scott Davies and Andrew Moore).**The majority of these slides were conceived and created by Scott Davies. Once you've got hold of a Bayesian Network, there remains the question of how you do inference with it. Inference is the operation in which some subset of the attributes are given to us with known values, and we must use the Bayes net to estimate the probability distribution of one or more of the remaining attributes. A typical use of inference is "I've got a temperature of 101, I'm a 37-year-old Male and my tongue feels kind of funny but I have no headache. What's the chance that I've got bubonic plague?".**Learning Bayesian Networks.**This short and simple tutorial overviews the problem of learning Bayesian networks from data, and the approaches that are used. This is an area of active research by many research groups, including Andrew and his students (see the Auton Lab Website for more details).**A Short Intro to naive Bayesian classifiers.**I recommend using Probability For Data Mining for a more in-depth introduction to density estimation and general use of Bayes classifiers, with naive Bayes classifiers as a special case. But if you just want the executive summary bottom line on learning and using naive Bayes classifiers on categorical attributes then these are the slides for you.**Short Overview of Bayes Nets.**This is a very short 5 minute "executive overview" of the intuition and insight behind Bayesian Networks. Read the full Bayes Net Tutorial for more information.**Gaussian Mixture Models.**Gaussian Mixture Models (GMMs) are among the most statistically mature methods for clustering (though they are also used intensively for density estimation). In this tutorial, we introduce the concept of clustering, and see how one form of clustering...in which we assume that individual datapoints are generated by first choosing one of a set of multivariate Gaussians and then sampling from them...can be a well-defined computational operation. We then see how to learn such a thing from data, and we discover that an optimization approach not used in any of the previous Andrew Tutorials can help considerably here. This optimization method is called Expectation Maximization (EM). We'll spend some time giving a few high level explanations and demonstrations of EM, which turns out to be valuable for many other algorithms beyond Gaussian Mixture Models (we'll meet EM again in the later Andrew Tutorial on Hidden Markov Models). The wild'n'crazy algebra mentioned in the text can be found (hand-written) here.**K-means and Hierarchical Clustering.**K-means is the most famous clustering algorithm. In this tutorial we review just what it is that clustering is trying to achieve, and we show the detailed reason that the k-means approach is cleverly optimizing something very meaningful. Oh yes, and we'll tell you (and show you) what the k-means algorithm actually does. You'll also learn about another famous class of clusterers: hierarchical methods (much beloved in the life sciences). Phrases like "Hierarchical Agglomerative Clustering" and "Single Linkage Clustering" will be bandied about.**Hidden Markov Models.**In this tutorial we'll begin by reviewing Markov Models (aka Markov Chains) and then...we'll hide them! This simulates a very common phenomenon... there is some underlying dynamic system running along according to simple and uncertain dynamics, but we can't see it. All we can see are some noisy signals arising from the underlying system. From those noisy observations we want to do things like predict the most likely underlying system state, or the time history of states, or the likelihood of the next observation. This has applications in fault diagnosis, robot localization, computational biology, speech understanding and many other areas. In the tutorial we will describe how to happily play with the mostly harmless math surrounding HMMs and how to use a heart-warming, and simple-to-implement, approach called dynamic programming (DP) to efficiently do most of the HMM computations you could ever want to do. These operations include state estimation, estimating the most likely path of underlying states, and as a grand (and EM-filled) finale, learning HMMs from data.**VC dimension.**This tutorial concerns a well-known piece of Machine Learning Theory. If you've got a learning algorithm in one hand and a dataset in the other hand, to what extent can you decide whether the learning algorithm is in danger of overfitting or underfitting? If you want to put some formal analysis into the fascinating question of how overfitting can happen, then this is the tutorial for you. In addition to getting good understanding of the overfitting phenomenon, you also end up with a method for estimating how well an algorithm will perform on future data that is solely based on its training set error, and a property (VC dimension) of the learning algorithm. VC-dimension thus gives an alternative to cross-validation, called Structural Risk Minimization (SRM), for choosing classifiers. We'll discuss that. We'll also very briefly compare both CV and SRM to two other model selection methods: AIC and BIC.**Support Vector Machines.**We review the idea of the margin of a classifier, and why that may be a good criterion for measuring a classifier's desirability. Then we consider the computational problem of finding the largest margin linear classifier. At this point we look at our toes with embarrassment and note that we have only done work applicable to noise-free data. But we cheer up and show how to create a noise resistant classifier, and then a non-linear classifier. We then look under a microscope at the two things SVMs are renowned for---the computational ability to survive projecting data into a trillion dimensions and the statistical ability to survive what at first sight looks like a classic overfitting trap.**PAC Learning.**PAC stands for "Probably Approximately Correct" and concerns a nice formalism for deciding how much data you need to collect in order for a given classifier to achieve a given probability of correct predictions on a given fraction of future test data. The resulting estimate is somewhat conservative but still represents an interesting avenue by which computer science has tried to muscle in on the kind of analytical problem that you would normally find in a statistics department.**Markov Decision Processes.**How do you plan efficiently if the results of your actions are uncertain? There is some remarkably good news, and some significant computational hardship. We begin by discussing Markov Systems (which have no actions) and the notion of Markov Systems with Rewards. We then motivate and explain the idea of infinite horizon discounted future rewards. And then we look at two competing approaches to deal with the following computational problem: given a Markov System with Rewards, compute the expected long-term discounted rewards. The two methods, which usually sit at opposite corners of the ring and snarl at each other, are straight linear algebra and dynamic programming. We then make the leap up to Markov Decision Processes, and find that we've already done 82% of the work needed to compute not only the long term rewards of each MDP state, but also the optimal action to take in each state.- In addition to these slides, for a survey on Reinforcement Learning, please see this paper or Sutton and Barto's book.
- Visual simulation of Markov Decision Process and Reinforcement Learning algorithms by Rohit Kelkar and Vivek Mehta.

**Reinforcement Learning.**You need to be happy about Markov Decision Processes (the previous Andrew Tutorial) before venturing into Reinforcement Learning. It concerns the fascinating question of whether you can train a controller to perform optimally in a world where it may be necessary to suck up some short term punishment in order to achieve long term reward. We will discuss certainty-equivalent RL, the Temporal Difference (TD) learning, and finally Q-learning. The curse of dimensionality will be constantly learning over our shoulder, salivating and cackling.- In addition to these slides, for a survey on Reinforcement Learning, please see this paper or Sutton and Barto's book.
- Visual simulation of Markov Decision Process and Reinforcement Learning algorithms by Rohit Kelkar and Vivek Mehta.

**Biosurveillance: An example.**We review methods described in other biosurveillance slides as applied to hospital admissions data from the Walkerton Cryptosporidium outbreak of 2000. This is work performed as part of the ECADS project.**Elementary probability and Naive Bayes classifiers.**This slide repeats much of the material of the main Probability Slide from Andrew's tutorial series, but this slide-set focuses on disease surveillance examples, and includes a very detailed description for non-experts about how Bayes rule is used in practice, about Bayes Classifiers, and how to learn Naive Bayes classifiers from data.**Spatial Surveillance.**This tutorial discusses Scan Statistics, a famous epidemiological method for discovering overdensities of disease cases.**Time Series Methods.**This tutorial reviews some elementary univariate time series methods, with a focus on using the time series for alerting when a sequence of observations is starting to behave strangely.**Game Tree Search Algorithms, including Alpha-Beta Search.**Introduction to algorithms for computer game playing. We describe the assumptions about two-player zero-sum discrete finite deterministic games of perfect information. We also practice saying that noun-phrase in a single breath. After the recovery teams have done their job we talk about solving such games with minimax and then alpha-beta search. We also discuss the dynamic programming approach, used most commonly for end-games. We also debate the theory and practice of heuristic evaluation functions in games.**Zero-Sum Game Theory.**Want to know how and why to bluff in poker? How games can be compiled down to a matrix form? And general discussion of the basics of games of hidden information? Then these are the slides for you. It might help you to begin by reading the slides on game-tree search.**Non-zero-sum Game Theory.**Auctions and electronic negotiations are a fascinating topic. These slides take you through most of the basic story of the assumptions, the formalism and the mathematics behind non-zero-sum game theory. It might help you to begin by reading the slides on game-tree search and Zero-sum Game theory with Hidden information available from this same set of tutorials. In this tutorial we cover the definition of a multiplayer non-zero-sum game, domination of strategies, Nash Equilibria. We deal with discrete games, and also games in which strategies include real numbers, such as your bid in a two player double auction negotiation. We cover prisoner's dilemma, tragedy of the commons, double auctions, and multi-player auctions such as the first price sealed auction and the second price auction. The math for the double auction analysis can be found at http://www.cs.cmu.edu/~awm/double_auction_math.pdf .**Introductory overview of time-series-based anomaly detection algorithms.**This simple tutorial overviews some methods for detecting anomalies in biosurveillance time series. The slides are incomplete: verbal commentary from the presentation has not yet been included as explanatory textboxes. Please let me (awm@cs.cmu.edu) know if you would be interested in more detail on these slides and/or access to the software that implements and graphs the various univariate methods. If I receive enough requests I will try to make both of the above available.**AI Class introduction.**A very quick informal discussion of the different kinds of AI research motivations out there**Search Algorithms.**What is a search algorithm? What job does it do and where can it be applied? We introduce various flavors of Breadth First Search and Depth First search and then looks at alternatives and improvements that include Iterative Deepening and Bidirectional Search. Then we look with furrowed brow at an idea called Best First Search. This will be our first view of a search algorithm that is able to exploit a heuristic function.**A-star Heuristic Search.**The classic algorithm for finding shortest paths given an admissible heuristic. We'll deal with the notion of admissibility (summary: admissible = optimistic). We show how you can prove properties of A*. We'll also briefly discuss IDA* (iterative deepening A*).**Constraint Satisfaction Algorithms, with applications in Computer Vision and Scheduling.**The tutorial teaches concepts from the AI literature on Constraint Satisfaction. Accompanying animations are in http://www.cs.cmu.edu/~awm/animations/constraint. This is a special case of uninformed search in which we want to find a solution configuration for some set of variables that satisfies a set of constraints. Example problems including graph coloring, 8-queens, magic squares, the Waltz algorithm for interpreting line drawings, many kinds of scheduling and most important of all, the deduction phase of minesweeper. The algorithms we'll look at include backtracking search, forward checking search and constraint propagation search. We'll also look at general-purpose heuristics for additional search accelerations.**Robot Motion Planning.**We review some algorithms for clever path planning once we arrive in real-valued continuous space instead of the safe and warm discrete space we've been sheltering in so far. We look at configuration spaces, visibility graphs, cell-decomposition, voronoi-based planning and potential field methods. Unfortunately some of the figures are missing from the PDF version.**Hill-Climbing, Simulated Annealing and Genetic Algorithms.**Some very useful algorithms, to be used only in case of emergency.