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support smart data strategy Because you are pioneering a developing new idea, albeit with existing and emerging technology, it is an iterative process requiring close collaboration between executive customers and IT solution providers You will be producing a capability that is best for your enterprise and that will produce superior results It is important to say this because we believe that, too often, the data ownership and responsibility is passed to IT or slips away from management control and visibility, getting lost in a sea of information technology We want to make explicit how to channel data, and how to optimize enterprise performance with complete visibility For instance, the DoD embarked on a strategy to employ enterprise resource planning software as a panacea for escaping a myriad of legacy systems supporting defense logistics The notion is that by having everyone on the same software, all organizations will be able to integrate operations Trouble began when organizations were asked to throw out their business rules and to adopt those embedded in the software First, the ERP software, for instance, was originally developed for private enterprise that is motivated by a completely different set of metrics than government enterprise, notably pro t motive versus constituent service utility motive Second, the solution of choice is often from a foreign vendor, making US defense systems and operations dependent on foreign software These large issues loom among many others and the circumstance has moved responsibility for enterprise data away from management and into the hands of supporting information technologists How did this happen Some key government executives and former military ag of cers ended up working for technology vendors as a part of the revolving door practice that compromises objectivity Alright, we know that American defense is dependent on foreign trading partners, customers, and allies It is not necessarily bad to engage foreign suppliers in US government programs However, one must ask what capabilities and assets should a nation own or be able to deliver domestically in order to remain secure These are executive questions that need constant attention as they affect policy and practice and, most important, data Accept the Premise Concluding the discussion about the value of data o the enterprise, accept the premise that all assets are ultimately expressed, described, and accounted for as data To optimize enterprise performance, the process is to take capital and material and, through enterprise processes, produce outcomes that are higher yield products and results, whereby the processes operate under constraints and the work is performed by people and technologies performing in concert The people are aligned with organizations, and the relationships among organizations are contractually bound From the viewpoint of the enterprise head, the enterprise creates certain data that is critical to its performance The enterprise receives data from external sources and transforms this data for internal purposes that translate into higher yield outputs The.

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Nonparametric approaches face problems of computational complexity Semiparametric approaches combine the advantages of both parametric and nonparametric approaches and are more popular Semiparametric approaches are computationally ef cient and provide locally optimal solutions A popular semiparametric density estimation approach is the expectation maximization (EM) algorithm The EM algorithm uses Gaussian mixture model and the maximum likelihood approach to estimate the pdf for a given data set The EM algorithm is well known to converge ef ciently to the local optimum Researchers from statistics and economics communities have recently shown interest in using maximum entropy (ME) measures for density estimation problems For example, it has been shown that an encoding and decoding approach based stochastic gradient ascent method for entropy maximization can be used to estimate probability densities It has also been proposed that a sequential updating procedure be used to compute maximum entropy densities subject to known moment constraints We may use a ME density approach to estimate error distribution in regression models All researchers have reported good results with the use of ME measures Others argue that ME densities have simple function forms that nest most of the commonly used pdfs, including the normal distribution, which is considered a special case as opposed to a limiting case All the procedures proposed and used in these studies converge to the local optimum and suffer from similar computational issues as that of the EM algorithm While the ME approach for density estimation has shown promise, current approaches cannot be applied directly to clustering problems in data mining These approaches assume either knowledge of data distribution or prior knowledge of movement constraints Since a typical application of density estimation in the data mining literature is likely to be an unsupervised learning problem, such prior knowledge may not be available In this case, we use a global search heuristic genetic algorithm for density estimation Genetic algorithms (GAs) are population based parallel search techniques that are likely to nd heuristic optimal solutions to optimization problems Unlike gradient search algorithms used in EM and ME density estimation, which are likely to get stuck in a local optimum, GAs are likely to provide solutions that are close to the global optimum We use GAs to estimate pdfs on a simulated data set using both the maximum likelihood (ML) formulation and the ME formulation Semiparametric Density Estimation Typical semiparametric density estimation consists of a nite mixture of the density models of k probability distributions, where each of the k distributions represents a cluster The value of k s usually less than the number of data points We use a Gaussian mixture model, where true pdf is considered to be a linear combination of k basis functions We use GAS for optimizing the nontrivial ML and ME optimization problems GAs are general purpose, stochastic, parallel search approaches that are used for optimization problems [8] We use oating point representation for our research.

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three times his stake with respective probabilities 025 and 015 His strategy is to bet $5 each time his payroll is more than $50 dollars and $10 otherwise De ne an appropriate Markov chain to compute the probability that Joe reaches his goal Also calculate the expected number of bets placed by Joe until he has gone broke or reached his goal 39 A training program consists of three parts, each having a length of one month Fifty percent of the starting students immediately pass the rst part after one month, 30% drop out before the end of the rst month and 20% take the rst part again Seventy percent of the last group pass the rst part after a second trial and the ther 30% still drop out Eighty percent of the students taking the second part pass this second part after the rst trial, 10% drop out after the rst trial and the other 10% move on after a second trial of the rst part Any student streaming into the third part of the training program will complete it successfully Calculate the probability that a starting student will be successful 310 Consider a nite-state Markov chain {Xn } with no two disjoint closed sets The matrix of one-step transition probabilities is called doubly stochastic when for each column the sum of the column elements equals 1 Verify that the equilibrium distribution of such a Markov chain is a uniform distribution 311 A gambling device is tuned such that a player who wins (loses) on a given play will win on the next play with probability 025 (050) The player pays $1 for each play and receives $250 for each play that is won Use Markov chain analysis to nd out whether the game is fair or not 312 A factory has a storage tank with a capacity of 4 m3 for temporarily storing waste produced by the factory Each week the factory produces 0, 1, 2 or 3 m3 waste with respective probabilities p0 = 1 , p1 = 1 , p2 = 1 , and p3 = 1 If the amount of waste 8 2 4 8 produced in one week exceeds the remaining capacity of the tank, the excess is specially removed at a cost of $30 per cubic metre At the end of each week there is a regular opportunity to remove waste from the storage tank at a xed cost of $25 and a variable cost of $5 per cubic metre The following policy is used If at the end of the week the storage tank contains more than 2 m3 of waste, the tank is emptied; otherwise no waste is removed Use Markov chain analysis to nd the long-run average cost per week 313 In a series of repeated plays, you can choose each time between games A and B During each play you win $1 or you lose $1 You are also allowed to play when your capital is not positive (a negative capital corresponds to a debt) In game A there is a single coin This coin lands heads with probability 1 ( = 0005) and tails with probability 2 1 + In game B there are two coins One coin lands heads with probability 1 and 2 10 the other coin lands heads with probability 3 If you play game B, then you must take 4 the rst coin when your current capital is a multiple of 3 and you must take the other coin otherwise In each play of either game you win $1 if the coin lands heads and you lose $1 otherwise (a) Use Markov chain analysis to verify that the long-run fraction of plays you win is 04957 when you always play game B (Hint : a three-state Markov chain suf ces) (b) Suppose you alternately play the games A, A, B, B, A, A, B, B, Use an appropriate Markov chain to verify that the long-run fraction of plays you win is 05064 This problem shows that in special cases with dependencies, a combination of two unfavourable games may result in a favourable game This paradox is called Parrondo s paradox after the Spanish physicist Juan Parrondo 314 At the beginning of each day, a crucial piece of electronic equipment is inspected and then classi ed as being in one of the working conditions i = 1, , N Here the working condition i is better than the working condition i + 1 If the working condition is i = N the piece must be replaced by a new one and such an enforced replacement takes two days If the working condition is i with i < N there is a choice between preventively replacing.

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