„True Optimization is the revolutionary contribution of modern research to decision processes“ – George Dantzig. Dachten Sie in der Schule im Mathematikunterricht nicht auch manchmal, „wofür braucht man das“? Mein Kollege, Dave R. Duling, hat auf dem SAS Global Forum 2015 einen Vortrag zu diesem Thema gehalten, über den ich
Optimization for machine learning is essential to ensure that data mining models can learn from training data in order to generalize to future test data. Data mining models can have millions of parameters that depend on the training data and, in general, have no analytic definition. In such cases, effective models
Optimization is a primary tool of computational statistics. SAS/IML software provides a suite of nonlinear optimizers that makes it easy to find an optimum for a user-defined objective function. You can perform unconstrained optimization, or define linear or nonlinear constraints for constrained optimization. Over the years I have seen many
This year's SAS Global Forum conference will take place April 18-21 at The Venetian in Las Vegas. For SAS/OR, SAS staff will present two Super Demos and three papers:
SAS will have a major presence at the 2016 INFORMS Conference on Business Analytics and Operations Research, which will be held at the Hyatt Regency Grand Cypress hotel in Orlando, FL on April 10-12. Many SAS staff will participate in this conference. SAS/OR, the SAS Global Academic Program, and JMP
さて、今回ご紹介する例は、最近議論が活発な、「機械（コンピューター）が人間の作業を奪う（？）」お話です。 機械は人間から仕事（今回の例では、仕事ではなく娯楽と言ったほうが近いかもしれません）を奪ったことになるのでしょうか？それとも、真の楽しみを味わえるように、単に単純労働から開放してくれただけなのでしょうか？ 昨今、人工知能がもたらす変化という文脈で行われている議論ですが、今回は、昔からある最適化アルゴリズムで、人間の仕事を奪います。皆さんでその意味を考えてみてください。 イギリスの諜報機関GCHQがクリスマスメッセージとして送った難解なパズルが公開されており、優秀な人たちを楽しませています。その第一問が、以下の「お絵かきロジック」です。日本でも一時期流行しました。イラストロジックなどとも言われ、私自身もトライした記憶があります。 このパズルそのものについては、他の情報源に頼って欲しいのですが、簡単に説明すると、それぞれのセルを黒か白で塗りつぶすパズルで、行と列に書かれている数字は、黒マスが連続している数を順番どおりに示している「手がかり」です。いくつかのセルはすでに黒く塗りつぶされていますが、それらはこのパズルの答えを一つに確定するために必要です。 一部の箇所は、それぞれの行や列の情報だけを見て解くことが可能です。例えば、７番目の行を見てみましょう。手がかりは、(7 1 1 1 1 1 7)です。すなわち、全部で 7 + 1 + 1 + 1 + 1 + 1 + 7 = 19 個の黒いセルが必要となり、最低ひとマスは間隔が空いていないといけないので、7個の固まりの間の個数を考慮すると、7-1=6 個の白マスが必要となります。この二つの数字を足すと、19 + 6 = 25 となり一行の列数とおなじ数にちょうどなります。したがって、この結果から直ちにこの行の全てがあきらかになります。 黒7, 白1, 黒1, 白1, ・・・ ついてきていますよね。 しかし、そうは簡単にいかない箇所のほうが多いでしょう。その場合には、手がかりから部分的にしか黒く塗りつぶせないことになります。例えば、一行目を見てください。ヒントから(7 + 3 + 1 + 1 + 7) + (5
The British spy agency GCHQ recently posted a grid-shading puzzle that the director sent out in his Christmas cards this year. The puzzle, shown here, is known as a nonogram and by various other names, including Paint by Numbers and FigurePic: Each cell is to be colored black or white,
Das Christkind, unser Analytics-Fuchs, ist auch irgendwie ein Pedant. Das Christkind, unser Pedant, ist auch irgendwie ein Chef mit all seinen Allüren. Heute wird nämlich eingeteilt, strammgestanden und dann gearbeitet. Dass dies den Engeln nicht gefällt, ist klar. Doch wenn der Chef spricht, beugen sich sogar Engel. Unsere Engelsprotagonisten von
Statistical programmers often need to evaluate complicated expressions that contain square roots, logarithms, and other functions whose domain is restricted. Similarly, you might need to evaluate a rational expression in which the denominator of the expression can be zero. In these cases, it is important to avoid evaluating a function
SAS/OR 14.1, which became available on July 14, delivers a number of new and enhanced features in optimization and simulation. These changes are designed to make SAS/OR even easier to use and to enable you to model and solve larger, more complex problems more efficiently. If you're using SAS/OR now,
SAS is hosting this year’s European Analytics 2015 conference in Rome November 9 – 11. This three-day inspiring event will give you the chance to boost your company’s analytics culture in an international environment to make sure your knowledge and expertise meet the demands of the digital era. But what if
Good Old Country-Style Optimization In an odd way, Imre Polik's recent post, How to solve puzzles? Peg solitaire with optimization, reminded me of one more reason why I like to eat at Cracker Barrel, an American chain of country-style restaurants.
The primary objective of many discrete-event simulation projects is system investigation. Output data from the simulation model are used to better understand the operation of the system (whether that system is real or theoretical), as well as to conduct various "what-if"-type analyses. However, I recently worked on another model
In the traveling salesman problem (TSP), a salesman must minimize travel distance while visiting each of a given set of cities exactly once. Recently, the TSP has generated some buzz in the popular media, after a blog post by Randy Olson. The tour shown was not quite optimal, and Bill
♦We learned this week that SAS is ranked #4 on Fortune's 100 Best Companies to Work For in 2015. This makes six straight years ranking in the top four (including twice at #1). ♦The March/April 2015 issue of Analytics Magazine includes a SAS company profile by my colleague Kathy Lange. As
Suppose someone needs a kidney transplant and a family member is willing to donate one. If the donor and recipient are incompatible (because of blood types, tissue mismatch, and so on), the transplant cannot happen. Now suppose two donor-recipient pairs A and B are in this situation, but donor A
Why do people steal ATMs? Because that's where the money is!!! While the old "smash-n-grab" remains a favorite modus operandi of would-be ATM thieves, the biggest brains on the planet typically aren't engaged in such endeavors (see Thieves Steal Empty ATM, Chain Breaks Dragging Stolen ATM, An A for Effort). And of
Just yesterday, Santa called my cell phone asking for a favor... Yes, Santa has my direct line, and I owe him (he once did me a solid, back in 1984, for Christmas, scoring me an awesome Optimus Prime Transformer). That's me there in the front - sporting plaid duds and
Do you have an Uncle Louie? Yep - we all do! You know what I mean - this guy: When my wife and I were planning to get married, we had all sorts of big decisions to make. Where would our future home be? How many kids would we have?
Nonlinear optimization routines enable you to find the values of variables that optimize an objective function of those variables. When you use a numerical optimization routine, you need to provide an initial guess, often called a "starting point" for the algorithm. Optimization routines iteratively improve the initial guess in an
Oil companies are being forced to explore in geologically complex and remote areas to exploit more unconventional hydrocarbon deposits. New engineering technology has pushed the envelope of previous upstream experience. No guidebook existed on how computing methodologies can contribute to E&P performance at reduced risk. Until now. A new book
Last week I showed how to find parameters that maximize the integral of a certain probability density function (PDF). Because the function was a PDF, I could evaluate the integral by calling the CDF function in SAS. (Recall that the cumulative distribution function (CDF) is the integral of a PDF.)
SAS programmers use the SAS/IML language for many different tasks. One important task is computing an integral. Another is optimizing functions, such as maximizing a likelihood function to find parameters that best fit a set of data. Last week I saw an interesting problem that combines these two important tasks.
The truncated normal distribution TN(μ, σ, a, b) is the distribution of a normal random variable with mean μ and standard deviation σ that is truncated on the interval [a, b]. I previously blogged about how to implement the truncated normal distribution in SAS. A friend wanted to simulate data
The April 2012 issue of ORMS Today contains a piece on "How analytics enhance the guest experience at Walt Disney World," by Pete Buczkowski and Hai Chu. While many of us are used to forecasting just one or two things (such as unit sales or revenue), Pete and Hai illustrate
I previously wrote about using SAS/IML for nonlinear optimization, and demonstrated optimization by maximizing a likelihood function. Many well-known optimization algorithms require derivative information during the optimization, including the conjugate gradient method (implemented in the NLPCG subroutine) and the Newton-Raphson method (implemented in the NLPNRA method). You should specify analytic
A popular use of SAS/IML software is to optimize functions of several variables. One statistical application of optimization is estimating parameters that optimize the maximum likelihood function. This post gives a simple example for maximum likelihood estimation (MLE): fitting a parametric density estimate to data. Which density curve fits the
