exponential random variable
... Exponential distribution (cont.) (1) Poisson process assumes that events occur uniformly throughout the interval of observation, i.e., there is no cluster of event. Thus, our starting point for observation does not matter. This due to the fact that the number of events in an interval of a Poisson p ...
... Exponential distribution (cont.) (1) Poisson process assumes that events occur uniformly throughout the interval of observation, i.e., there is no cluster of event. Thus, our starting point for observation does not matter. This due to the fact that the number of events in an interval of a Poisson p ...
CASE STUDY: Classification by Maximizing Area Under ROC Curve
... of classifiers. Namely, a classifier which attains higher AUC is preferable to a lower AUC classifier. This motivates us directly maximize AUC for obtaining a classifier. Such a direct maximization is rarely applied because of numerical difficulties. Usually, computationally tractable optimization m ...
... of classifiers. Namely, a classifier which attains higher AUC is preferable to a lower AUC classifier. This motivates us directly maximize AUC for obtaining a classifier. Such a direct maximization is rarely applied because of numerical difficulties. Usually, computationally tractable optimization m ...
Sample Final #3 Solution
... intersections of the streets are vertices, and the streets themselves are edges. If Sam delivers his mail without doubling back or retracing his steps, such a route must be an Euler path, since it requires crossing every edge exactly once. However, we know that an undirected graph with more than two ...
... intersections of the streets are vertices, and the streets themselves are edges. If Sam delivers his mail without doubling back or retracing his steps, such a route must be an Euler path, since it requires crossing every edge exactly once. However, we know that an undirected graph with more than two ...
5. Random Processes
... The probability density functions for random variables in time have been discussed, but what is the dependence of the density function on the value of time, t, when it is taken? If all marginal and joint density functions of a process do not depend upon the choice of the time origin, the process is ...
... The probability density functions for random variables in time have been discussed, but what is the dependence of the density function on the value of time, t, when it is taken? If all marginal and joint density functions of a process do not depend upon the choice of the time origin, the process is ...
Probabilistic Skyline Operator over sliding Windows
... SSKY Techniques presented in Section IV to continuously compute q-skyline (i.e., skyline with the probability not less than a given q) against a sliding window. Naïve approach on basic problem is about 20 times slower than SSKY, so it’s been ruled out ...
... SSKY Techniques presented in Section IV to continuously compute q-skyline (i.e., skyline with the probability not less than a given q) against a sliding window. Naïve approach on basic problem is about 20 times slower than SSKY, so it’s been ruled out ...
Asymptotic Approximations
... When exact sampling distributions for estimators and test statistics are not available, econometricians often rely on approximations obtained from asymptotic arguments. These approximations are sometimes quite accurate and can often be constructed without a complete specification of the population d ...
... When exact sampling distributions for estimators and test statistics are not available, econometricians often rely on approximations obtained from asymptotic arguments. These approximations are sometimes quite accurate and can often be constructed without a complete specification of the population d ...
POSITIVE DEFINITE RANDOM MATRICES
... numerical algorithms. The diagonal elements of the matrix have often specified significance. The correctness of such numerical algorithm can be proven if we are able to choose a positive definite matrix at random with uniform distribution. The space of all positive definite matrices is, however, a c ...
... numerical algorithms. The diagonal elements of the matrix have often specified significance. The correctness of such numerical algorithm can be proven if we are able to choose a positive definite matrix at random with uniform distribution. The space of all positive definite matrices is, however, a c ...
Algorithms Lecture 5 Name:___________________________
... Θ(nlog n) “advanced” sorting algorithms: Merge sort and Quick Sort. Consider why a divide-and-conquer sort might be more efficient. Assume that I had a simple Θ(n2) sorting algorithm with n = 100, then there is roughly 1002 / 2 or 5,000 amount of work. Suppose I split the problem down into two small ...
... Θ(nlog n) “advanced” sorting algorithms: Merge sort and Quick Sort. Consider why a divide-and-conquer sort might be more efficient. Assume that I had a simple Θ(n2) sorting algorithm with n = 100, then there is roughly 1002 / 2 or 5,000 amount of work. Suppose I split the problem down into two small ...
Fisher–Yates shuffle
The Fisher–Yates shuffle (named after Ronald Fisher and Frank Yates), also known as the Knuth shuffle (after Donald Knuth), is an algorithm for generating a random permutation of a finite set—in plain terms, for randomly shuffling the set. A variant of the Fisher–Yates shuffle, known as Sattolo's algorithm, may be used to generate random cyclic permutations of length n instead. The Fisher–Yates shuffle is unbiased, so that every permutation is equally likely. The modern version of the algorithm is also rather efficient, requiring only time proportional to the number of items being shuffled and no additional storage space.Fisher–Yates shuffling is similar to randomly picking numbered tickets (combinatorics: distinguishable objects) out of a hat without replacement until there are none left.