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Indunction learning and decision tree learning [closed]

Is it appropriate to say that decision tree learning is a type of induction learning?
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13 views

Incorporating Risk Aversion in Bayesian Expected Loss functions

In Berger's Statistical Decision Theory and Bayesian Analysis, he presents the following expected loss function for decision theory: $\rho(\pi^*,a)=\int_\Theta L(\theta,a)d\pi^*(\theta)$ Where ...
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1answer
25 views

Association rules or classifier for product modeling for queries

I have a set of products P {1...n} which are rated on a goodness scale G ={1...100} (G10 is more good than G5). Each product has a set of features F {1....m}, now I want to learn a model for ...
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6 views

Is a Bayes randomized rule always a Bayes nonrandomized rule?

Given a prior distribution on the parameter space, is a Bayes rule among all randomized rules (nonrandomized rules are special randomized rules) always a nonrandomized rule? I.e. Is a Bayes randomized ...
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20 views

Are these independent: the sample, randomized rule, and random variable having the prior distribution on the parameter space?

In section 1.3 of Bickel and Doksum's Mathematical Statistics 2006, the risk function of a nonrandomized rule $d$ is the expectation of loss of the rule wrt the random sample. $$ R(\theta, d) := ...
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1answer
39 views

Is there a distribution where the data is generated from a decision process?

Sometimes my data is the result of the decisions each individuum of the observed population made: how much invest, how much gambled etc. The outcome would be a metric variable: money spent in total by ...
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0answers
10 views

admissibility under weighted error loss implies admissibility under square error loss

Show that admissibility of a decision rule under weighted square error loss implies it's admissibility under square error loss. Weighted Square error loss = $\frac {(d(x) - ...
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1answer
37 views

admissibility of bayes rule

How to show that for a binomial(n, p) distribution, the MLE X/n is admissible under square error loss? The Bayes rule undr square error loss with beta($\alpha, \beta$) prior is X+$\alpha$/ (n ...
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0answers
4 views

Optimal intertemporal allocation of bets based on estimated returns

Each day, an investor predicts the day's stock-market return in the morning, generating a point estimate and prediction interval, and chooses to bet an amount $B_t$ on the market that day based on her ...
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1answer
55 views

Bayes estimator under LINEX loss?

Suppose we are trying to estimate a real valued parameter under the linear exponential (LINEX) loss. Suppose we have some prior $g$ that has finite mean, variance and a moment generating function. ...
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0answers
10 views

Existence of Minimax rule

If a minimax point does not exist, a minimax rule will not exist? But can a non-randomized rule be minimax in this situation? My set of risk points are: S = {(10,5),(8.4,5.4),(9.6,5.6), (8,6)).
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1answer
21 views

Bayesian calculation of parameter multiplying normal

I am interested in a model like: $y_{i} = \sum_{k\in K}{\beta_{k} z_{k}}$, with $z_{k} \tilde{} N(\mu_{k}, \sigma_{k})$. where $\beta \equiv(\beta_{k})_{k\in K}$ is not known, but all else is. I ...
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1answer
44 views

Detecting a consistent pattern in a dataset via Decision Trees and cross-validation

Assume a classification problem where there are two classes and the aim is to detect a consistent pattern which successfully separates the input dataset regardless of how we divide it into training / ...
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3answers
120 views

Is 'fair statistics' a thing?

Given that statistics can often be abused to deliberately present 'facts' to support a pre-existing viewpoint. (Lies, damned lies and statistics). And given confirmation bias. Is there an ...
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0answers
11 views

Optimal Number of Entries in Contest of Skill

Objective: I'm looking for the optimal number of unique entries in a contest of skill with monetary prizes. Description: The contests vary from as little as 20 entries up to 10,000+ entries. You ...
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26 views

How does weka's decision table handle numerical (continuous) output and numerical inputs?

I've been using WEKA's decision table majority classifier in order to do a feature selection on a data set with both numerical (continuous) and categorical inputs, and numerical (continuous) output. ...
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0answers
51 views

Intuition behind the Stein's paradox [duplicate]

I had read wiki and some sources. jmanton's blog, Wasserman's blog the background is that: You have Xi ∼ N(θi, 1), and we want to estimate the each θi. Where Xi are ...
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2answers
207 views

Drawing numbered balls from an urn

PROBLEM There is an urn with a set of balls where each ball is labeled with a different integer. The numbers on the balls are known and are not a range of integers. For example the set of balls could ...
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2answers
116 views

Bayes decision theory: Classification error probability

In Bayesian decision theory: Given $\omega_1$ and $\omega_2$ as two classes for classification, $P\left( \omega_1 \right)$ and $P\left( \omega_2\right)$ their prior probabilities, $x$ the feature ...
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1answer
57 views

Loss function that relates ROPE with HDI?

In Doing Bayesian Data Analysis (link to the book) and Bayesian Estimation Supersedes the t-Test, J. Kruschke proposes using the following criterion to reject or accept the null hypothesis in a ...
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0answers
39 views

bayes optimum decisions and loss functions

In this question, one of the comments discusses the benefits of using Bayes optimum decision rules coupled with loss functions rather than using other performance metrics such as sensitivity. My ...
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1answer
57 views

Decision function problem based on the logistic function

Suppose we have a bunch of a sampled pairs $(x_1,y_1)...(x_n,y_n)$ with the $y_i =\pm1$. Then consider the decision function $h(x) = -1$ if $p(x)=\frac{1}{1+e^{-x}}\leq0.5$, and $h(x) = 1$ if $p(x) ...
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0answers
22 views

Rearranging 2 discriminant function to solve for 1 parameter (to derive a decision boundary)

I have a task where I want to classify patterns from 2 classes where the samples are drawn from a bivariate Gaussian distribution. I use the 2 discriminant functions ($g_1$ and $g_2$) to classify the ...
2
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1answer
108 views

A case of understanding customer behavior

Suppose I have a big online company, and many of my customers churned (i.e. they were paying, and then stopped). My goal is to understand why each of them churned. First I identify the complete set ...
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0answers
68 views

Given 3 discriminant functions I was able to classify 2D patterns, but how do I plot decision boundaries via matplotlib?

I have implemented the discriminant function and was able to classify the 2D patterns (via Python), but I have troubles thinking about an approach to plot the decision boundaries. Hope anyone has an ...
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1answer
91 views

Formal justification of Bayesian inference as a model for belief

I remember a proof that Bayesian probability theory is the only valid method for representing beliefs, it went something like we represent belief by some non-negative function over some domain of ...
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48 views

Best Methods for data-mining neuroimaging data with 1000 subjects

I am part of a team tasked with performing exploratory analysis of a large data set containing neuro-imaging scans. For each scan I will likely calculate some variable that relates to brain function - ...
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0answers
74 views

Plotting a decision boundary separating 2 classes using Matplotlib's pyplot

I could really use a tip to help me plotting a decision boundary to separate to classes of data. I created some sample data (from a Gaussian distribution) via Python NumPy. In this case, every data ...
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0answers
23 views

Admissibility and domination for estimators

Watching a video by the "mathematicalmonk" on the web, I was wondering how to answer this kind of questions: Given $X_1,\ldots,X_n\sim \mathcal{N}\left(\mu,\sigma^2\right)$. Assume that $\mu$ is ...
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0answers
39 views

What is a robust way to find the max of $n$ independent, non-identical random variates?

Suppose I observe $n$ random variates along with their variance (but not mean) and I'd like to select the one with the largest mean as frequently as possible. The procedure must be memoryless--you ...
3
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1answer
46 views

Given $n$ different univariate non-normal sample sets calculate for a new sample, $x$, which it most likely belongs to [duplicate]

Say you have $n$ different, non-normal, potentially overlapping data sets of samples. Maybe their densities look something like: and you are given a new sample $x$, how would you decide to which of ...
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0answers
83 views

Maximizing returns - A Bayesian approach

I want to design a Bayesian model for a simple asset allocation problem. Say I can buy $a_i$ amounts of $N$ assets. The return values of these assets are given by random variables $r_i$ with known ...
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1answer
122 views

How to incorporate constraints in random forest output

Suppose I am doing random forest classification of labels $A$,$B$,$C$,$D$. There is some theoretical ordering to this output such that when $A$ is more likely than $B$, $B$ is also more likely than ...
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0answers
117 views

Computing Confidence in A/B testing

First of all, I'm fairly new to Decision Theory and my question might be rather too simple for the experts. I am having some issues in computing confidence for A/B Testing. I will first explain the ...
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0answers
26 views

determining the number of variables in the kernal of a U-stat

I'm working through some problems on deriving U-statistics, and I am unsure about determining the number of samples (random variables?) that are needed for the kernel of a given U-stat. For example: ...
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0answers
91 views

Showing that a statistic is ancillary for a parameter

Working through a HW problem, and a hint is that for a decision rule $$T(X) = \frac{X_{(1)} + X_{(n)}}{2}$$ Then $$T - \bar{X} $$ is ancillary. Intuitively this makes complete sense, but I am ...
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1answer
161 views

How do I combine multiple prior components and a likelihood?

Lets imagine I am comparing two groups of animals (treatment/control). There is previous data from cell cultures indicating the treatment should have a positive effect. This gives me "prior component ...
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1answer
44 views

Markov Decision Process and its generality

My major is CS and I have a question about Markov decision process. I have been reading a book, planning with markov decision process an AI perspective. While reading it, I have a question regarding ...
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1answer
156 views

Prove/counter example: A minimax decision rule is always Bayes wrt some proper prior

Not sure whether the claim is true or false. If claim is true, intuitively, it might have something to do with "least favorable priors", but am not able to figure out the connection. If claim is ...
2
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1answer
104 views

What is a loss function in decision theory?

My notes define a loss function as the 'cost' incurred when the true value of $\theta$ is estimated by $\hat\theta$. What kind of cost is it talking about? monetary cost? or is it something related to ...
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1answer
102 views

Using decision trees with very infrequent outcomes

I am working on decision tree model and a value in dependent variable (churn) is very less. we have 1.5 lac records and only 1700 records have churn = 1. While using decision tree model, tree is not ...
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1answer
2k views

Decision boundary plot for a perceptron

I am trying to plot the decision boundary of a perceptron algorithm and am really confused about a few things. My input instances are in the form [(x1,x2),target_Value], basically a 2-d input instance ...
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0answers
50 views

Example Of Strict von Neumann Inequality

Let $r(\pi, \delta)$ denote the Bayes risk of an estimator $\delta$ with respect to a prior $\pi$, let $\Pi$ denote the set of all priors on the parameter space $\Theta$, and let $\Delta$ denote the ...
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0answers
123 views

Is the expected value a valid decision-making method in a very short term?

This might be related to game theory more than statistics, but I decided to ask this question here. Let's assume you're offered a lottery. There are a hundred balls in a bowl: 99 white balls and one ...
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0answers
76 views

Optimizing “twenty questions”-like decision tree queries

I'm looking for an algorithm which can optimize the selection of queries used to build a decision tree. However, unlike most decision trees, I am constrained to ask the same set of questions for every ...
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1answer
74 views

Value of Information for a simple investment problem

Assume the following problem: You're deciding whether to invest into an opportunity with uncertain cost $c$ and value $v$. The cost has been estimated to be normally distributed with 90% CI between 1 ...
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1answer
104 views

The meaning of translation completeness w.r.t a random variable

I stumbled upon this term in McFadden - Analysis of qualitative choice behavior (page 111). It is said that "A random Variable $X$ is translation complete if for a function h of bounded ...
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1answer
68 views

Question about proof for luce choice axiom w.r.t. conditional probability

In Luce (1959) the choice axiom is definied, that for a finite subset $T$ of $U$ such that, for every $S\subset T$, $P_S$ is defined. If $P(x,y)\ne 0,1$ for all $x,y\in T$, then for $R\subset ...
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1answer
181 views

What technical language to describe the degree to which probabilities are likely to be modified by future data?

I'm trying to reason about something I call "estimate stability," and I'm hoping you can tell me whether there’s some relevant technical language, so that I can learn about it and then write a ...
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42 views

Sampling to maximize model accuracy

Suppose you have a relatively small random sample and have a corresponding model $\ Y$ ~ $\operatorname{Bernoulli}(p_i) $ $\ \operatorname{logit}( \hat{p_i} )=\hat{\beta}*X$ and now want to draw a ...