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Sunday Feb 05, 2006

New Location!

Check out my new blog location for Predict This! at bloglines.com

Technorati Profile

Technorati Profile

Monday Jan 16, 2006

The Accuracy Paradox



Warning

Today, let me try and convince you to avoid the accuracy metric in favor of other metrics such as precision and recall.

Accuracy is often the starting point for analyzing the quality of a predictive model. Accuracy is also probably the first term that comes to mind when non-experts think about how to evaluate the quality of a prediction. As shown below, accuracy measures the ratio of correct predictions over the total number of cases evaluated.

What about the business relevance of accuracy? Surprisingly, this is a difficult question. It seems obvious that the ratio of correct predictions over all cases should be a key metric for determining the business impact of a predictive model. Yet, the value of the accuracy metric is dubious. In fact, it is often trivially easy to create a predictive model with high accuracy, and such trivial models can be useless despite of high accuracy. Similarly, when comparing the business impact of two alternative predictive models, it may well be the less accurate model that is more beneficial to the user organization.

Let's review an example predictive model for an insurance fraud application. To prevent payment on fraudulent claims all cases that are predicted as high-risk by the model will be investigated by fraud experts. The insurance has devised a predictive model that predicts fraud with some degree of accuracy. And in order to evaluate the performance of the model the insurance has created a sample data set of 10,000 claims. All 10,000 cases in the validation sample have been carefully checked and it is known which cases are fraudulent. Now, to analyze the quality of the model, the insurance uses the table of confusion below.

Definition of Accuracy


Predicted Negative

Predicted Positive

Negative Cases

9,700

150

Positive Cases

50

100


Table 1: Table of Confusion for Fraud Model M1Fraud.

The accuracy for model M1Fraud computes to:

Accuracy of Model M<sub>1</sub><sup>Fraud</sup>

With an accuracy of 98.0% model M1Fraud appears to perform fairly well. However, the Accuracy Paradox lies in the fact that accuracy can be easily improved to 98.5% by always predicting "no fraud". The table of confusion and the accuracy for this trivial “always predict negative” model M2Fraud are shown below.


Predicted Negative

Predicted Positive

Negative Cases

9,850

0

Positive Cases

150

0

Table 1: Table of Confusion for Fraud Model M2Fraud.

Definition of Accuracy

Model M2Fraud reduces the rate of inaccurate predictions from 2% to 1.5%. This is an apparent improvement of 25%. Although the new model M2Fraud shows fewer incorrect predictions and markedly improved accuracy, as compared to the original model M1Fraud, the new model is obviously useless. The alternative model M2Fraud does not offer any value to the insurance company for preventing fraud, and clearly, the less accurate model is more useful than the more accurate model. The inescapable conclusion is that high accuracy is not necessarily an indicator of high model quality, and therein lies the Accuracy Paradox of predictive analytics. High accuracy does not necessarily lead to desirable business outcomes, and model improvements should not be measured in terms of accuracy gains. It may go too far to say that accuracy is irrelevant for assessing business benefits but I advise against using accuracy when evaluating predictive models.


Hazmat

Saturday Jan 14, 2006

Seminar on Computational Learning and Adaptation


Stanford University - Palm Drive On the 7th of December 2005, I had the opportunity to present at Stanford University about the "Business Impact of Predictive Analytics". I paste the Seminar on Computational Learning and Adaption announcement below. The seminar is chaired by Professor Pat Langley, and a number of members of his research staff and other guests also participated in the seminar.

The discussion during and after my presentation hit a couple of interesting points. One was that it would be interesting to explore the possibility of going beyond the prediction of a single target variable to predict sets of variables.

Professor Pat Langley For example, a predictive capability might predict the risk of an event happening, the cost of either outcome of the event happening or not happening, the cost of taking action to prevent the event, and the probability that the action might prevent the event. This set of variables together would allow for a more comprehensive analysis of business impact.

For instance, in an insurance fraud prediction and prevention application, it is desirable to predict, for each claim, the probability of fraud, the predicted cost of fraud, the cost of taking action to prevent fraud, and the probability that the action will prevent payment on the fraudulent claim.



Seminar on Computational Learning and Adaptation



  Business Impact of Predictive Analytics

Dr. Tilmann Bruckhaus


Chief Architect, Data Mining and Analytics
Sun Microsystems

Tilmann.Bruckhaus@Sun.Com
 

In commercial applications of predictive modeling, the ultimate objective is typically to maximize Return On Investment (ROI). However, literature, conferences, and training often stops short of providing techniques for ROI maximization. With an apparent lack of know-how for maximizing ROI, analysts often have to rely on technical metrics, such as ROC, accuracy, precision, or similar metrics to optimize predictive models. In this presentation, I will explore the problem of assessing the ROI for predictive analytics applications, break down the drivers of ROI, and show how to compute ROI. I will also present an example ROI analysis to demonstrate that one predictive model can have negative or positive ROI based on the business context in which it is used, even though technical quality metrics of the predictive model do not change.


Date: Wed., Dec 7, 2005 

Time: 4:15-5:30PM

Place: Cordura 100


Return to the seminar schedule

Friday Jan 13, 2006

AI Application Programming


AI Application Programming Techniques I recently reviewed an interesting book for Stickyminds.Com:

AI Application Programming, 2nd edition
Author: M. Tim Jones
Pages: 473	Published: 2005
Publisher: Charles River Media	ISBN: 1584504218
M. Tim Jones' book “AI Application Programming” is a practical and inspiring introduction into a variety of artificial intelligence programming techniques. This book is ideal for readers who want to become familiar with a variety of artificial intelligence application programming techniques without delving into much detail on any one technique.

Locust Swarm - Swarm Intelligence M. Tim Jones reviews 15 Artificial Intelligence (AI) programming techniques from Classifier Systems to Simulated Annealing. Jones begins by reviewing the history of AI from the 1940s to the present, and he concludes his book by a review of the present state of AI. The main part of the book is dedicated to the overview of programming techniques.

Each technique is described in general terms to convey the purpose and motivation of each technique, and to provide the context of who developed the technique and why. With this background we move on to a brief overview of how the procedure operates, guided by diagrams and small example problems. One of the most useful resources this book provides is source code in the C programming language for a simple implementation of each technique. Jones walks us through the more interesting functions of each implementation to illuminate programming techniques used to transform the technique from idea to executable. The complete source is provided on a CD which is included with the book. There is an even balance between the general description of each technique and the source code review.

Alife - Artificial Life The A-Star path finding algorithm is covered first in Jones book, followed by the newer Simulated Annealing technique which aims to find global maxima instead of suboptimal local maxima. Next, we find the fascinating Particle Swarm Optimization method which can track moving targets, and the Adaptive Resonance Theory which finds application in personalization solutions that can help recommend likely choices in shopping application and other similar systems. The Classifier System serves to link conditions to actions, and the Ant Algorithm explores environments to find hidden targets. The book also covers the equally useful techniques of Neural Networks, Reinforcement Learning, Genetic Algorithms, Artificial Life, Rule-Based Systems, Fuzzy Logic, Natural Language Processing, Bigram Model, and finally Agent-Based Software.

Fuzzy Logic This book has many advantages not easily found in other texts. The organization of the material is clear and simple. One chapter is dedicated to each technique with a few well-designed subsections with various details. Each chapter stands on its own, and the reader can easily focus on just a small number of techniques of interest, or skip over some of the techniques.

Working source code in the C programming language is included for each technique, and this code makes the book immediately useful for anyone beginning to develop software with artificial intelligence capabilities. The source code of the key functions of every programming technique is reproduced in the book as part of each chapter along with the author's review of the code at a fairly detailed level.

Every AI programming technique is also illustrated with a variety of diagrams, tables and session transcripts from program runs. Jones' writing style is unassuming and straight forward, and that is all the more helpful considering the complexity of the subject matter. Another key feature is the fairly broad selection of over a dozen different techniques, helping readers appreciate the diversity of practical artificial intelligence programming techniques.

Thursday Jan 12, 2006

Too Good To Be True


Split (The town in Croatia) The greatest danger to success with Predictive Analytics may be to over-estimate the predictive power of a predictive model. One problem that can lead to over-estimating predictive power is over-fitting. Over fitting occurs when a predictive model is trained to memorize training data so well that the model will not perform well when scoring new data. Machine Learning algorithms typically split training data internally to test for and to avoid overfitting. This internal splitting is an important safe guard but it is advisable to take the additional precaution of setting a hold out data set aside against which the quality of a trained model can be tested.

A hold out data set is created by splitting your available historical data set into two subsets, one for training, and one for validation. It is crucial that the validation data set faithfully mimics new data coming in for scoring in the production environment. What is important is to exclude any inputs that carry information that is not available when the model is deployed, and also to exclude any information from the training data set that provides clues about the to-be-predicted outcomes for the validation data. If you make a mistake your validation will be meaningless.

Churn For example, consider anecdotes I heard at KDD04, Directions 2005 and ICDM05. A predictive model was being developed for a churn prediction application, and an account code was used as an input. The model validated with excellent precision but it was found later that the account code contained information about whether the account was active. This made it too easy for the model to predict churn because accounts that are canceled due to churn then become inactive. The account code is therefore an illegal input, at least if the account code represents current status as opposed to the historical status as of the time before the churn event occurred.

An image which includes a tank. In a military application the goal was to train a model to identify tanks in imagery. This model too performed exceedingly well but it was later found that all the training images containing tanks were taken at a different time of day than those images that did not contain tanks, and the validation data had the same problem. Again, it was easy for the model, in fact unrealistically easy, to identify the presence of tanks by assessing the overall brightness of the image.

I have yet to meet an experienced practitioner in Predictive Analytics who does not admit to accidentally using illegal inputs or allowing hints about outcomes in the validation hold-out data set to spill into the training data set.

Wednesday Jan 11, 2006

Predictive Analytics vs. Information Retrieval


Predictive Analytics and Information Retrieval (IR) are two technologies used in data mining. However, they are used for different purposes, as the table below illustrates. One common aspect is that the quality of both types of solutions can be measured with Precision and Recall metrics. See the previous post for more information about precision and recall.


Information Retrieval

Predictive Analytics

General Purpose

Multi-database, open-ended research

Prediction, classification and scoring

Scope of Results

Wide

Narrow

Type of Results

Entire Documents from various sources, such as internal databases, document collections, and Google results.

A single value, such as a risk percentage (e.g., "42%"), classification ("red", "blue", "green"), or predicted value. (e.g., "54.2")

Setup

Connect to source databases, then perform any desired query.

Develop a custom model for each task.

Typical Uses

Research background info on a given technical issue.

Pinpoint high-risk situations among hundreds or even millions of known cases.

Mechanism

Sophisticated indexing of source documents.

Discover complex patterns in high-dimensional spaces.

How are results found?

Matching against a user-supplied ad-hoc query.

Matching against mathematical patterns that were learned during a training phase.

Strengths

Flexibility - handle any ad-hoc query on the fly.

Automation - provide answers without user intervention..

Tuesday Jan 10, 2006

How are Precision and Recall Calculated?


Precision Calculating precision and recall is actually quite easy. Imagine there are 100 positive cases among 10,000 cases. You want to predict which ones ore positive, and you pick 200 to have a better chance of catching many of the 100 positive cases. You record the IDs of your predictions, and when you get the actual results and tally up how many times you were right or wrong. There are four ways of being right or wrong:

  • TN / True Negative: case was negative and predicted negative
  • TP / True Positive: case was positive and predicted positive
  • FN / False Negative: case was positive but predicted negative
  • FP / False Positive: case was positive but predicted negative

Makes sense so far? Now you count how many of the 10,000 cases fall in each bucket, say:



Predicted Negative

Predicted Positive

Negative Cases

TN: 9,760

FP: 140

Positive Cases

FN: 40

TP: 60



Now, your boss asks you three questions:
  • How many percent of your predictions were correct?
    You answer: the "accuracy" was (9,760+60) out of 10,000 = 98.2%
  • How many percent of the positive cases did you catch?
    You answer: the "recall" was 60 out of 100 = 60%
  • How many percent of positive predictions were correct?
    You answer: the "precision" was 60 out of 200 = 30%

Saturday Dec 10, 2005

The Exception to the Rule


Cold Reasoning Mr Spock Machine learning technology enables computers to find complex patterns in historical data and to model these patterns so that they can be applied to current data in order to predict future outcomes.

That is something humans do as well when we learn. How is machine learning different and similar to human learning? It seems obvious that machines do not have human intuition, and that they are cold reasoning machines which follow predefined, hard-coded, simplistic reasoning patterns.

Machine learning is changing the way machines analyze data and make predictions. I wonder whether machine learning is slowly beginning to add rudimentary human-like qualities to computer-based analysis. Here are three parallels between information processing by humans and in machines.

Daniel Kahneman Let's look at intuition and reasoning first. Daniel Kahneman, winner of the Nobel Prize in economics, says there are two basics systems involved when humans make economic decisions: intuition and reasoning. Is there anywhere in machine learning where something like intuition and reasoning is taking place? I think there are some interesting parallels to neural networks and rule induction, two key concepts in machine learning. Rule induction makes predictions that can easily be traced through a model and explained step by step. You can identify all the rules in a rule base and see how they contributed to making a prediction. For example, you may find rules like "if income is above $100,000 then credit risk is low". That sounds a little like reasoning to me.

NMOS transistor, designed to a 2 lambda rule set, for 0.8 micron process Neural networks, on the other hand, make reliable predictions but these are difficult to interpret, like human intuition. In both cases one cannot trace the data to the conclusion in the same language used to define the problem. However, one can trace predictions by neural networks back to training cases that are similar to the current case, and therefore lead to similar predictions. In human intuition, one may be able to think back of past experiences where similar situations lead to the outcome that intuition predicts.

There might be other parallels, too. Human intuition is instantaneous and effortless, whereas reasoning requires more time and effort. Do neural networks make predictions more quickly than decision trees or rule sets? To evaluate a neural network arithmetic calculations are made. To evaluate a rule set decisions must be made by evaluating conditions. I have not compared execution times for neural networks and decision trees but it would be interesting to analyze this question. Other interesting questions are how much time is required to first train neural networks and rule induction models, and how much time is required to update these models with incremental new training cases. I believe we may find parallels here as well. Incremental updating of neural networks may be faster as it involves updating a set of weights, whereas updating a decision tree or rule set may involve reorganizing the entire model. I do not have formal empirical or theoretical results, though.

Rorschach Inkblot Lastly, let's look at humor. This is really just a guess but here goes. It seems that humor may be a mechanism for mediating between intuition and reasoning. A joke leads us through a line of reasoning that leads to a logic conclusion. We follow the rules and decisions carefully but at the end we arrive at a conclusion that is dramatically different from the result of a quick intuitive analysis of the situation. Humor may aid decision making by identifying the exception to the rule.

Thursday Nov 03, 2005

Concept Drift


Shopping Cart In Predictive Analytics, the term concept refers to the quantity you are looking to predict. For example, in a fraud detection application the target concept may be a binary attribute FRAUDULENT with values "yes" or "no" that indicates whether a given transaction is fraudulent. Or, in a weather prediction application, there may be several target concepts such as TEMPERATURE, PRESSURE, and HUMIDITY. More generally, the term concept can also refer to other phenomena of interest other than the target concept, such as an input, but in the context of concept drift we are specifically talking about the target concept.

The term Concept Drift, then, refers to unforeseen changes over time in the phenomenon of interest. For example, online shopping behaviors change over time. Let's say you want to predict weekly merchandise sales, and you have developed a predictive model that works to your satisfaction. The model may use inputs such as the amount of money spent on advertising, promotions you are running, and other metrics that may affect sales. What you are likely to experience is that the model will become less and less accurate over time - you will be a victim of concept drift. In the merchandise sales application, one reason for concept drift may be seasonality, which means that shopping behavior changes seasonally. You will likely have higher sales in the winter holiday season than during the summer.

Weather To prevent deterioration in prediction accuracy over time you will have to refresh your model periodically. One approach is to retrain your model with new data, and the other approach is to also add new inputs before retraining your model. For our sales prediction application you may be able to reduce concept drift by adding information about the season to your model. By providing information about the time of the year you will likely reduce rate of deterioration of your model, but you likely will never be able to prevent concept drift alltogether. This is because actual shopping behavior does not follow any static, finite model. New factors may arise at any time that influence shopping behavior, the influence of known factors may change, and interactions between known factors may change as well.

Concept Car The bottom line is that concept drift cannot be avoided if you are looking to predict a complex phenomenon that is not governed by fixed laws of nature. All processes that arise from human activity, such as socioeconomic processes, and biological processes are likely to experience concept drift. Therefore, periodic retraining, also known as refreshing of your model is inescapable.

See also "The problem of concept drift: definitions and related work", by Alexey Tsymbal, Department of Computer Science, Trinity College Dublin, Ireland, tsymbalo@tcd.ie, April 29, 2004)

Thursday Oct 20, 2005

High Dimensionality


Railroad Museum What's the right analytical tool for your business problem? The answer is governed in part by the "dimensionality" of the phenomenon you are dealing with. Let's start with a simple situation.

When you calculate the arrival time for a train you are working with 3-dimensional data: distance, speed, and time. You can predict arrival time if you know speed and distance. The formula is in the form d = v * t, using 2 inputs (v and t) to predict 1 output (d).

A problem in three dimensions is hardly "high dimensional". How about a dozen dimensions - where do we deal with about 12 dimensions? A cake recipe lists about as many quantities to control the outcome of a process. A chemical production process may also be measured in about as many dimensions to control it's outcome: temperature, pressure, humidity, quantities of substances added, mix rate, etc. How about a process that is governed by a hundred dimensions? Consider specs for automobiles or stereo systems . You will find dozens of measurements in this type of spec. These measurements may tell you something about the product, with each measurement describing something relevant to purchase and use. Thousands of dimensions? Think of all the data columns in all the databases in a commercial organization, such as a mid-sized company, or a business unit of a large corporation. Tens of thousands of dimensions? The number of variables in large software system at execution time comes to mind.

Cake High-dimensional problems are hard to describe and control. Throughout the centuries, laws of nature have been discovered which enable us to make predictions based on a small number of variables. The fewer inputs the more general the theory. For example, d = v * t is a formula with only three dimensions. More recently, statistical methods have enabled us to accept or reject hypotheses based on measurements of more dimensions, say 6 or even 20.

Neural Network Although traditional statistical analysis does not scale to hundreds of dimensions, recent developments in a field of statistics called Computational Learning Theory have extended the reach of statistics to such high-dimensional problems. Kernel Methods have well understood statistical properties and can handle highly-dimensional inputs. Decision Trees are also based on sophisticated statistical evaluations. Another algorithm in the machine learning tool box is the Neural Network. All of these classes of computational learning algorithms can guide commercial decisions based on hundreds of dimensions. As one may expect, low-dimensional problems can also be solved by machine learning techniques, and traditional statistics can handle them as well.

Considering the above, a reasonable strategy for solving business problems emerges. If you cannot solve a problem with a simple formula, formulate a hypothesis and accept or reject it using statistics. If this fails, you may want to try machine learning. You will need more data to apply hypothesis testing than you need to apply a known formula, and to use machine learning you will need more data again. Traditional statistics can work with data sets of about 30 observations or more. Machine learning commonly uses thousands of observations. There are also rules of thumb providing guidance on selecting among these approaches: traditional hypothesis-testing is the work horse of the chemical and mechanical industries, whereas machine learning is popular in the financial sector, retail, and customer relationship management (CRM).

Friday Oct 07, 2005

Complexity


One can argue that the essence of business is to provide customers with simple solutions to complex problems. Ants exhibit complex behavior. Complexity can be seen in anthills, human brains, and stock markets, but complexity also abounds in the business environment. From engineering to marketing, sales and customer support, business is governed by complexity; and data mining is an essential tool for supporting such complex business functions. Complex systems exhibit behavior that cannot be explained in simple ways, and that makes it hard to manage business systems. The most difficult support needs are those that involve making predictions. For example, how do you predict sales, product ship dates, marketing response rates, or service quality? Let's look at predicting customer support escalations as an example, and explore how data mining can increase the profitability of a customer support business function.

Complexity (Wikipedia) Increasingly, service processes are highly automated and a very large number of cases are handled simultaneously. Consider a complex service business where thousands or millions of cases may be active throughout a year, a day, or even at any moment. Most cases are handled within established boundaries but there are notable exceptions. In exceptional but not so rare cases, a service case escalates. By definition, these escalations are marked by customer pain, and they frequently require executive involvement, and they may cause excessive costs. How can this complex business function be supported to prevent escalations? One approach is to fix the complex system to remove the possibility of escalations. A complementary approach, and this is the approach I discuss here, is to predict escalation risk for each case, and to proactively engage in high-risk situations to forestall escalations. It is possible to predict the escalation risk of each case with so-called predictive analytics solutions.

Escalation (Wikipedia) Think of a recent escalation you have been involved in. In my experience, a moderate proactive investment could have avoided any specific catastrophic escalation. The problem is that if you handle thousands or millions of cases you cannot give each one any significant incremental attention. You need to identify cases in need of attention with laser-like focus. It can be profitable to establish proactive processes which engage only for identified high-risk situations. But how can you determine whether that proactive process is profitable? We're in luck here, because the situation is really quite simple. Profitability depends on only three quantities: prevention cost, escalation cost, and prediction precision.

Some examples will help to confirm this. Say prevention cost is $5,000 for engaging a customer proactively, escalation cost is $80,000 due to penalties, and prediction precision is 35%, then you will make an average profit of $23,000 on each case you address proactively: (0.35 * ($80,000 - $5,000)) - (0.65 * $5,000) = $23,000. At a precision of 10% your profit plummets to $3,000, and below 7% your profit turns negative because you spend more on prevention than you save on prevented escalations. Similarly, if prevention cost is $10 and escalation cost is $75 then your break-even point for predicition precision will be at 13%.

International Conference on Data Mining 2005, Huston, USA I hope you found this overview of data mining as a tool for complex business problems useful. If you want to learn more you may be interested in a research paper I coauthored on maximizing the ROI of predictive analytics: "Predicting Software Escalations with Maximum ROI" by Charles X. Ling, Shengli Sheng, Tilmann Bruckhaus, and Nazim H. Madhavji. This paper has been accepted for publication at The Fifth IEEE International Conference on Data Mining, Sponsored by the IEEE Computer Society, Houston, Texas, USA, 27 - 30 November 2005. I plan to post again soon about the nasty property of "high dimensionality" and how data mining can help you deal with it.

Friday Sep 30, 2005

Nasty Properties


Wikipedia: Chaos Theory Data mining can solve problems with "nasty properties" that make them hard to tackle. These nasty properties are chaotic behavior, high complexity, high dimensionality, concept drift, and poor data quality. Ordinary software code and traditional statistical methods cannot deal well with these issues. Let's look at these issues more closely.

Wikipedia: Butterfly Effect Chaotic behavior refers to situations where a small change in the inital configuration of a system can lead to dramatically different bahavior over time. For example weather simulation has this property. One often quoted story tells of how Edward Lorenz ran a weather simulation for days and was very satisfied with the result. He wanted to make his prediction even more precise by adding additional precision to the inputs he fed into the simulation. So he changed the input variables by a tiny amount. However, surprisingly, he found that the results he obtained were not an improved version of his earlier result but rather drastically different. Lorenz had discovered the chaotic nature of weather: if a butterfly flaps its wings in the Amazonas this tiny and remote difference in atmospheric conditions can lead to a chain reaction of changes that, in the end, may lead to a tornado hitting the USA. This phenomenon is known the Butterfly Effect.

Data mining avoids explicitly modeling the mechanisms that governs the output. Weather simulation involves modeling how atmospheric variables affect each other and lead to the resulting weather. Instead, data mining uses standard machine learning algorithms to learn what input patterns lead to different outputs. In other words, simulation will run a very large number of iterations to arrive at the expected weather three days in the future. Data mining instead looks at inputs available today and learns from historical records what the most likely weather situation will be like three days, without computing all of the weather patterns in between.

Over the next few days, I plan to post additional information on the other "nasty" properties.

Wednesday Sep 21, 2005

Favorite Data Mining Resources: Website and Book


One of my favorite web resources on data mining is KDNuggets.com. KDNuggets covers Data Mining, Knowledge Discovery, Text Mining, and Web Mining. There is an informative newsletter you can sign up for. The newsletter keeps you current on new developments, articles published, products, resources, jobs, and events:

KDNuggets

Data Mining Book A good book on data mining and knowledge discovery is "Data Mining - Practical Machine Learning Tools and Techniques" by Witten and Frank. This book covers techniques and algorithms, input and output formats, data preparation and transformations, and the open source machine learning environment Weka.

Monday Aug 29, 2005

Predictive Analytics


I created this blog to share thoughts about my field of expertise. I have been working on Predictive Analytics since 1999 and over time this has become the primary focus of my work. More generally, I am interested in Data Mining, Machine Learning, Data Analytics, and Business Intelligence.

If you check into my blog you can expect to find some of my current thinking on topics I see as important to these subjects.

Tilmann Bruckhaus

Tilmann Bruckhaus

Dr. Tilmann Bruckhaus
Chief Architect, Data Mining and Analytics
Sun Microsystems, Inc.
4220 Network Circle, M/S USCA22-117
Santa Clara, CA 95054 US
Phone x31867 / +1 408-404-4714
Mobile 408-887-6208
Fax x15840
Email Tilmann.Bruckhaus@Sun.COM