Download ISYE 6501 Final Exam Questions and Answers (Solved Papers) and more Exams Nursing in PDF only on Docsity!
(Solved Papers)
Factor Based Models - Correct Answers ✅classification, clustering, regression. Implicitly assumed that we have a lot of factors in the final model Why limit number of factors in a model? 2 reasons - Correct Answers ✅overfitting: when # of factors is close to or larger than
of data points. Model may fit too closely to random effects
simplicity: simple models are usually better Classical variable selection approaches - Correct Answers ✅1. Forward selection
- Backwards elimination
- Stepwise regression greedy algorithms Backward elimination - Correct Answers ✅variable selection; classical Opposite of forward selection. Start with model with all factors, at each step find worst factor and remove from model. Continue until no more to add, # of factor threshold is satisfied. Remove factors at the end that were not good enough
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Forward selection - Correct Answers ✅variable selection; classical Start with model with no factors, at each step find best new factor to add. Continue until none bad enough to remove, # of factor threshold is satisfied. Remove factors at the end that were not good enough Stepwise regression - Correct Answers ✅variable selection; classical Combination of forward selection and backwards elimination. Start with all or no factors. Each step remove/add a factor. As it continues, after adding in new factor we eliminate right away any factors that may be good. Helps model adjust when new factors are added, goodness values change Ways of determining if factors are good enough in variable selection - Correct Answers ✅p-value, Rsquared, AIC, BIC Greedy algorithm - Correct Answers ✅At each step, it does the one thing that looks best without taking future options into consideration. Good for initial analysis
- Forward selection
- Backwards elimination
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- T = limit or "budget" on how large the sum of squared errors can get. Budget will be used on most important coefficients
- Combination of lasso and ridge regression.
- Variable selection benefits of LASSO
- Predictive benefits of ridge regression Ridge Regression - Correct Answers ✅- Method of regularization by limiting the sum of the squares of the coefficients. Will reduce the magnitude of coefficients, not the number of variables chosen.
- The quadratic term in ridge regression tends to shrink the coefficient values i.e Whatever the basic regression model coefficients would be, the quadratic constraint pushes them toward zero or regularizes them. Design of Experiments (DOE) - Correct Answers ✅How can we still have a representative sample of each combination of factors, while only surveying 600 people? How to determine which of the several factors are most important to predicting someone's answers? comparison to measure difference
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control for other factors and effects blocking factors that account for the variation between factors (red sports car vs red minivan example) A/B testing - Correct Answers ✅Whenever we want to choose between 2 alternatives. As long as the following 3 things are true: 1st, we need to be able to collect a lot of data quickly enough to get an answer in time to use it. 2nd, the data we collect has to be from a representative sample of the whole 3rd, the amount of data we collect has to be small compared to the total population we want to use the answer on. Before modeling and before collecting data (Full) Factorial Design - Correct Answers ✅Test every combination of variables in an experiment to find each one's effect, and interaction effects on the outcome. Fractional Factorial Design - Correct Answers ✅A subset of combinations to test - selected combinations give same result as full factorial design i.e a balanced design
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What needs to be the case when matching data to a probability distribution to gain insight based on how the distribution is derived? - Correct Answers ✅The only information we have about a data point is the response, or when it would be hard to collect and analyze additional information What is the Bernoulli distribution is useful to model? - Correct Answers ✅A single event. i.e flipping a coin, will it rain or not?, will I get this job offer or not? Only really useful when you put many of them together (flip a coin 10,000 times) Describe a Bernoulli distribution in terms of a coin toss test - Correct Answers ✅Probability (p) that a single coin flip comes up heads and probability (1-p) that the coin comes up tails Define a Binomial distribution - Correct Answers ✅The probability of getting x yes answers out of n independent Bernoulli trials, each with the probability p When is the normal distribution useful as an estimate for the Binomial distribution? - Correct Answers ✅When n is large, and for modeling errors (predictive models)
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What is the question to describe a Geometric distribution? - Correct Answers ✅How many (Bernoulli) trials are needed before we get an answer of a certain type? What is the Poisson distribution good at modeling? - Correct Answers ✅Random arrivals of people to lines, queues etc
- The function gives the probability that x people do arrive given the average arrival rate (lambda)
- assumes arrivals are independent, and identically distributed (i.i.d) What is the Exponential distribution good at modeling? - Correct Answers ✅The time between arrivals or trials (inter-arrival time) How are the Poisson and Exponential distributions related? - Correct Answers ✅If arrivals are Poisson, with arrival rate lambda, then the time between arrivals (inter-arrival time) follows the exponential distribution (1/lambda = inter-arrival) The same is true if inter-arrival time is exponential
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When k > 1, the Weibull is good for modeling what? - Correct Answers ✅When failure rate increases with time Things that wear out What does the memoryless property mean? - Correct Answers ✅It doesn't matter what's happened in the past, all that matters is where we are now. Tire wearing out IS NOT memoryless Queuing Model - Correct Answers ✅Refer to the simulation we did - that's a much more complicated type of problem, so it's a simulation. 2 types of simulation (in regards to property) - Correct Answers ✅1) deterministic
- stochastic Deterministic simulation - Correct Answers ✅never vary - no randomness in the system.
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Stochastic simulation - Correct Answers ✅system includes randomness, so variation will occur 2 types of simulation (in regards to change) - Correct Answers ✅1) continuous-time: changes happen continuoulsy (disease propagation)
- discrete-event: changes happen at discrete time points Parts of a simulation (discrete-event) - Correct Answers ✅entities modules actions resources decision points statistical tracking Validating a simulation what 2 points should you consider? - Correct Answers ✅Look at average AND variance Non-parametric test for simulations' replications - Correct Answers ✅Use the same random numbers when possible...so that
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Adding a random value (up or down) to model-predicted imputed data - Correct Answers ✅Perturbation. Less accurate on average, but more accurate w/ variability Optimization is good for ____________ analytics - Correct Answers ✅Prescriptive: given what I know, and what I predict, what's the best course of action to take Optimization models are comprised of 3 components: - Correct Answers ✅1) Variables
- Constraints
- Objective Function - measure the quality of a solution Variables, constraints and objective function for optimization for linear regression - Correct Answers ✅variables = a0,a1,...am (coefficients) constraints = none objective function = minimize the squared error in the model estimates
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Variables, constraints and objective function for optimization for LASSO regression - Correct Answers ✅(standard regression, w/ 1 constraint added) variables = a0,a1,...am (coefficients) constraints = restrict the sum of the variables objective function = minimize the squared error in the model estimates Variables, constraints and objective function for optimization for Ridge regression - Correct Answers ✅variables = a0,a1,...am (coefficients) constraints = restrict the sum of the squares of the variables objective function = minimize the squared error in the model estimates Variables, constraints and objective function for optimization for elastic net - Correct Answers ✅variables = a0,a1,...am (coefficients) constraints = combines the 2 terms into 1 (restrict sum and sum of squares of variables) objective function = minimize the squared error in the model estimates
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Variables, constraints and objective function for optimization for Arima - Correct Answers ✅variables = mu, theta, phis constraints = none objective function = minimize the prediction error Variables, constraints and objective function for optimization for GARCH - Correct Answers ✅variables = omega, Beta i, gamma i constraints = none objective function = minimize the prediction error Variables, constraints and objective function for optimization for clustering - Correct Answers ✅variables = coordinates for cluster centers, and binary variables for whether each data point is part of each cluster constraints = each data points must be assigned to exactly 1 cluster objective function = minimize the sum of distances from each data point to its cluster center constant coefficients and variables from statistics and optimization points of view - Correct Answers ✅Statistics: xij are variables
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aj are constant coefficients Optimization: xij are constant coefficients aj are variables Linear Program - Correct Answers ✅An optimization model where the objective function is a linear function of the variables, and the constraints are linear equations and/or linear inequalities in terms of the variables. EASIEST Convex quadratic program - Correct Answers ✅An optimization model where the objective function is to minimize a convex function (or maximize a concave function) and the constraints define a convex set of feasible solutions. 2nd EASIEST Convex Optimization Program - Correct Answers ✅Optimization model where the objective function is a linear function of the
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Network model - Correct Answers ✅a Linear program Model where locations (nodes or vertices) are connected by arcs or edges, with flow on the arcs from node to node. Stochastic optimization model - Correct Answers ✅An optimization model that accounts for randomness or uncertainty. Types of stochastic optimization methods - Correct Answers ✅1) be conservative, adding value theta
- scenario modeling Dynamic programming structure - Correct Answers ✅system divided into states - exact situation and their values decisions - choices of next state Bellman's equation - determine optimal decisions When decisions have probabilities of next state instead = Stochastic dynamic program
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Optimization Algorithm - Correct Answers ✅1) initialization - choose an initial (starting) solution
- repeat a 2 stage process:
- starting w/ current solution, find a vector of relative changes to make to each variable (improving direction), and
- make changes in that direction some amount (stepsize) to get the new solution New solution = old solution plus the improving direction X the stepsize Iterate til it doesn't change much, or time is up When do you use hypothesis tests? - Correct Answers ✅When you know the underlying distribution What type of test should you conduct if you do not know the underlying distribution - Correct Answers ✅non-parametric tests
