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Questions tagged [decision-theory]

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bayesian decision making - comparing expected loss

The problem is like this: Suppose that I am considering which country should I invest on, country A and country B, based on their GDP growth rate $\alpha$. There are two possible choices for each ...
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0answers
12 views

Deciding on split points

I have an input variable[x] which is continuous and another output variable[y] which is categorical with two categories[Good, Bad]. I am wondering if there is a scientific way to find the split ...
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1answer
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Classification: Barking up the right 'decision tree'? [closed]

I have a really wide dataset (lots of columns). In any given use case, I would take a list of rows and want to classify the key features (columns) that are most prevalent within this sample. Am I ...
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1answer
24 views

Choose one of two normal distribution that will give the probability of biggest value when sampling it

Suppose you have two (or more) normal distributions with different mean and variance. You can draw only one sample of only one of the available distributions. Your goal is to get the biggest value ...
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12 views

Shadow significance

I've faced specific issue recently and kindly ask you to help. Imagine standard linear supervised learning framing for binary classification problem (X,y, OLS, p-vals, etc.). One can develop common ...
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1answer
14 views

What is minCases in C5.0Control using R

from Package (C5.0 Decision tree Using R ) definition "minCases : an integer for the smallest number of samples that must be put in at least two of the splits." I very confuse about it . Please ...
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23 views

Finding the type II error given the type I error for a minimax decision rule with 0-1 loss

Assume a two world state ($\Omega=\left\{ \omega_{0},\omega_{1}\right\}$ ) scenario and that we are given the [continuous] ROC curve $\left\{ \left(\alpha\left(\theta\right),1-\beta\left(\theta\right)\...
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16 views

Decision Tree from Agglomerative Clustering

I have agglomerative clustering done. I want to convert it to a decision tree so I can figure out the cluster very quickly. How to do so? A tedious approach (bad, I know): Take the top ...
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1answer
63 views

Admissibility does not imply minimax

The answer to minimax estimator explains why minimax does not imply admissibility. The relevant statement is from https://www.stat.berkeley.edu/~yuekai/201b/lec6.pdf which says, minimaxity does not ...
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1answer
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DECISION TREE : How to calculated for repeat decision noded such as this picture (C5.0 Algorithm -Decision tree)

I confused about decision tree such as this picture why repeat decision node.Could you please explain that decision tree. thank you
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0answers
36 views

How many sunrises are worth observing?

The one-sun version of Laplace's sunrise problem provides a Bayesian argument that, if on all $n$ mornings in recorded history the Sun has risen, its probability of doing so tomorrow is $\frac{n+1}{n+...
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1answer
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How to categorize data as others if training set is not available?

I run into a problem. I am using the decision tree to classify the incident category based on the short description the user has used while logging the ticket. I have the training data only for 5 ...
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How can I run a decision tree algorithm with a specific hierarchy of variables and with many missing values?

I asked students in learning groups what their biggest learning problem was "today" for each learner. The biggest problem could either be "motivational" (=motivation problem) or cognitive (="knowledge ...
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0answers
29 views

Model fitting vs minimizing expected risk

I'm confused about the mechanics of model fitting vs minimizing risk in decision theory. There's numerous resources online, but I can't seem to find a straight answer regarding what I'm confused about....
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2answers
88 views

Why is the risk function defined to be the expectation of loss function?

In decision theory, we define the risk associated with a particular predictor function as the expected value of the loss function. Since the input and output are considered random variables therefore ...
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1answer
49 views

Decision tree without the “tree”

I would like to construct something like a decision tree. However, instead of using "recursive partitioning" to build a tree, I would like to find an optimal set of "global" splits. For example, in a ...
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0answers
21 views

Can additional iterations of backward induction as described affect optimal policy?

Consider a game with the following properties: Single player Finite number of game states (after the player arrives at a terminal state, he or she can begin again from the start state; the player can ...
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2answers
57 views

Hypothesis testing using spectra

How does hypothesis testing work when a measurement is not a single number, but an entire spectrum? For instance, suppose we want to distinguish a species of plant based on its absorption spectrum. ...
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0answers
40 views

What problem or game are variance and standard deviation optimal solutions for?

For a given random variable (or a population, or a stochastic process), mathematical expectation is the answer to a question What point forecast minimizes the expected square loss?. Also, it is the ...
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1answer
69 views

Bayes estimate with weighted square error loss

First, let $T(x)$ be an estimator of $g(\theta)$ and assume we have a square error loss function defined as $$L[g(\theta),T(x)]=[g(\theta)-T(x)]^2$$ Then the posterior expected risk of $T$ is $$\...
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1answer
52 views

Minimize mis-classification - 0 - 1 output

I am studying logistic regression from the book Advanced Data Analysis from an Elementary Point of View which states the following on page 280: “We minimize the mis-classification rate by ...
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0answers
12 views

Predicting Value versus predicting likelihood of value in auction

I am in a situation where I am trying to estimate what price will win an auction. I am trying to decide whether I should build a model to a) predict the price directly, or b) given a price as data, ...
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2answers
238 views

Does a density forecast add value beyond a point forecast when the loss function is given?

Density forecasts are more universal than point forecasts; they provide information on the whole predicted distribution of a random variable rather than on a concrete function thereof (such as ...
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1answer
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Multidimensional Bayes point estimates

Consider the posterior distribution $p(\theta|x)$. We aim to find a "good" estimate of the random variable $\theta$. The Bayes risk associated with the loss function $L(\hat{\theta}, \theta)$ is ...
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3answers
208 views

MAP is a solution to $L(\theta) = \mathcal{I}[\theta \ne \theta^{*}]$

I have come across these slides (slide # 16 & #17) in one of the online courses. The instructor was trying to explain how Maximum Posterior Estimate(MAP) is actually the solution $L(\theta) = \...
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0answers
36 views

Decision tree ,information gain and overfitting

If i use the information gain in order to evaluate the best split in a decision tree, why using a binomial split reduces the risk of overfitting ? Is the information gain test misleading if we have a ...
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3answers
268 views

Does a Bayes estimator require that the true parameter is a possible variate of the prior?

This might be a bit of a philosophical question, but here we go: In decision theory, the risk of a Bayes estimator $\hat\theta(x)$ for $\theta\in\Theta$ is defined with respect to a prior distribution ...
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0answers
73 views

The math behind Spearman-Karber method

A number of methods in my field use the Spearman-Karber method to estimate the minimum level of a variable needed for 50% success on a task. In addition to the original work, I have tried to increase ...
2
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2answers
264 views

comparing distributions - bayesian decision analysis

I am attempting to use Bayesian analysis to compare distributions to help with decision analysis - when to treat a patient based on a blood measurement X. Here you can see 1000 samples from two ...
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0answers
41 views

Decision tree: faster way than entropy calculations (by hand)

Background I'm trying to understand how decision trees are made, for which I studied entropy calculations and information gain. Let's take a look at an example: ...
5
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1answer
419 views

Different definitions of Bayes risk

I'm having trouble understanding the proper definition of Bayes risk. Let the data/variate $x \sim P(X|\theta)$, $\theta\in \Theta$, $\pi$ be a distribution on $\Theta$ (prior), $\hat \theta(x)$ be ...
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0answers
174 views

Why can't the complete class theorem be easily generalized to all locally-compact spaces?

So I was reading Christian P. Robert's The Bayesian Choice, going through the constellation of results related to complete class theorems, and I don't see why all of them are necessary. In particular, ...
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0answers
81 views

Optimal strategy for a combinatoric dice game

The game can be played at https://xcvd.github.io/dice-game/ The player gets 12 throws of 3 dice and chooses a grid to place these throws in (there are 6*6*6=216 possible throws). Each throw ...
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0answers
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Controlling the accuracy of a classifier by giving no answer

I have a multi-class classifier based on a feature vector $x$ (for example using logistic regression). Say I have accuracy $a\in[0;1]$. Now my classifier is allowed to sometimes refuse to answer. I ...
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1answer
86 views

Why Loss function has to be bounded from below (statistical decision theory)?

In statistical decision theory the loss function $L(\theta, a)\ge-K > -\infty$ is often chosen for technical convenience (e.g. See [1] p.3 ). Can anyone explain why the above condition is ...
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1answer
471 views

What do the thresholds on x and y axis of ROC curve represent?

There is a detailed explanation of what the AUC of an ROC curve is here. However I have searched high and low for an explanation regarding what the X and y axes of the ROC curve are. I have understood ...
2
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1answer
77 views

Machine learning methods for exploring relationships for a continuous response variable

I would like to explore a model to predict the value of a continuous response variable, from a set (around 100) of explanatory variables. I do not want to apply PCA like feature reduction, because I ...
2
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1answer
50 views

Choose parameters ,such that MSE of an estimator is constant

I have an estimator : $X = (X_1,X_2,...,X_n)$ are iid and have distribution $B(1,\theta)$ $T(X) = X_1 + X_2 + ... + X_n$ I need to find such value of constants $\alpha$ and $\beta$ s.t MSE of ...
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0answers
46 views

Decision making under uncertaintly

In decision making under uncertainly we have these criterion 1- maximin criterion 2- minimax criterion 3- maximax criterion Now I want real life example to illustrate all of these criterion (I ...
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3answers
196 views
+50

Why care so much about expected utility?

I have a naive question about decision theory. We calculate the probabilities of various outcomes assuming particular decisions and assign utilities or costs to each outcome. We find the optimal ...
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1answer
108 views

Comparing estimators of equal risk

I'm attending a course in mathematical statistics and it seems the lecturer tacitly assumes that given estimators $T_1,T_2 : \Omega \to \Lambda$ of a parameter $g : \Theta \to \Lambda$, a loss ...
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0answers
50 views

Bayesian Decision Making (for particular problem)

I've read several papers why p-values should be replaced by Bayes factors and trying to use them. What I have: say, I have matrix of 2000 rows and 1000 columns. In each column I need to make a ...
3
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0answers
63 views

Where can I find a measure-theoretic statement of the Von Neumann-Morgenstern axioms?

Most of the discussion of the Von Neumann-Morgenstern axioms I have seen isn't fully formal - in fact, a lot of it only applies to finite probability spaces. Where can I find a more general discussion,...
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0answers
57 views

How to bet on a binary event based on the markov transition matrix, state probabilities and the odds

There is a coupon full of football matches for a given day from a bookkeeper. I have scrapped another website and i have aquired continuous history of a particular match between ...
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3answers
660 views

How are estimators like the Horvitz-Thompson Estimator derived?

The Horvitz-Thompson Estimator is usually given by: $$ \hat{Y}_{HT} = \sum_{i=1}^n \pi_i ^{-1} Y_i $$ The proof that it is unbiased is trivial to do. In additional, there exists other estimators out ...
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1answer
58 views

Is there any “Intro to Statistics” for business and mangement use?

I am looking for an "Introduction to Statistics" to apply to business and management. Can someone recommend a source they have used (maybe in their MBA or similar studies) that is available online (...
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1answer
115 views

Relationship between “Logistic regression + L1 regularization” and PCA

This is the experiment I have done. My data contain several hundreds of samples but with over 20k features per sample, so I used logistic regression + L1 regularization (LR+L1) to fit a linear ...
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1answer
73 views

Random interpretation of prediction

I am trying to build a binary classifier. Normally I'd build a model that predicts $P(y = 1 \mid x)$ and choose a threshold. I classify $1$ if predicted probability $\ge$ threshold. What about this ...
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0answers
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Bayesian Decision Theory - Self Study [duplicate]

Consider a naive Bayes classier with a binary class $Y ∈ {0, 1}$ and three binary features $X_1, X_2, X_3$ ∈ {0, 1}. You are given a set $D$ of $n$ training examples, i.e. D={$(x^{(1)}_1, x^{(1)}_2, ...
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116 views

Utility theory approach in decision making for Gaussian variables

Consider the following problem:- In nutshell there are 3 decisions $d_1,d_2,d_3$ and 3 effects $S_1,S_2,S_3$ after the decision has been made. Each effect can occur with a given probability. In ...