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Questions tagged [isotonic]

isotonic means monotone, either increasing or decreasing. Use this tag for isotonic regression (monotone regression) and other forms of order-restricted inference, like hypothesis testing with ordered alternatives.

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Testing if three proportions follow hypothesized ordering

I have a set of $n$ samples, and each sample $i$ is labeled with three binary characteristics $a_i,b_i,c_i\in \{0, 1\}$. I'm trying to test the hypothesis that the proportion with $a_i = 1$ is the ...
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Is perfect isotonic probability calibration realistic?

I work with a labelled tabular dataset of about 1 million observations, with the target being binary. The dataset is heavily imbalanced - about 0.5% positive class. I have trained a gradient boosting ...
StrLdn's user avatar
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How to calculate MEC90 or MEC95 with isotonic regression in R?

Several studies calculate the minimum effective concentration (MEC), volume (MEV), or dose (MED) as MEC90 or MEC95 and base the calculation on a study by Pace and Stylianou. One of the best ...
barerd's user avatar
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4 votes
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Ordinal correlation vs. univariate isotonic regression - practical differences?

Ordinal correlation statistics such as Spearman's $\rho$ or Kendall's $\tau$ allow us to measure the association of two variables while considering only the ranks of the observations. Isotonic ...
Trisoloriansunscreen's user avatar
1 vote
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861 views

Post hoc analysis for 3x2 cross tab analysis?

Apologies if this is straight forward. Also please note that I am using SPSS and don’t know how to use R/code. I’m a physician doing clinical research. I’m doing an analysis regarding 3 different ...
Feras Akbik's user avatar
1 vote
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How to optimize a ML model as a function of the relationship between the predictions in the training set?

I am working on a proof-of-concept model for estimating the state-of-health of batteries based on logged voltage and current time series. It is an unsupervised problem in that I do not have access to ...
JohanGustafsson's user avatar
4 votes
1 answer
803 views

Should Scikit-Learn CalibratedClassifierCV isotonic mode use bucketed rates instead of the actual targets?

This is less a question about sklearn's implementation, and more theoretical. I find it weird that we'd do isotonic regression against target values in {0, 1} because that could result in very jagged ...
Alexander Soare's user avatar
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calibration of classifier scores: isotonic regression

I am investigating the isotonic regression approach to calibrate the scores from a classifier. If I understand correctly, we do the following. First, we get the calibration plot (or reliability curve),...
ABK's user avatar
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In isotonic regression, why do we use linear interpolation

Isotonic Regression solves following optimization problem. given ordered inputs $x_1,x_2,\dots x_m$ i.e., $x_1 \leq x_2 \dots \leq x_m $ and corresponding target variables $y_1,y_2, \dots y_m$, ...
manifold's user avatar
1 vote
1 answer
204 views

Bivariate isotonic regression on unbalanced grid

I would like to do classic isotonic regression on bivariate data (that is to say, x with two columns). The function biviso of package Iso is very fast but requires a balanced grid. I would like to do ...
Xu Wang's user avatar
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7 votes
2 answers
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Monotonic splines in Python [closed]

I am trying to find a procedure to fit data monotonically in Python. The data won’t be necessarily monotonic. I just would like to achieve a monotonic fit because of theoretical assumptions. I ...
Eaglez's user avatar
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Understanding probability calibration with isotonic regression in sklearn

After reading sklearn manual it was not very obvious for me to understand how Isotonic regression works in the case of probability calibration (using CalibratedClassifierCV). I briefly read sklearn's ...
Rodvi's user avatar
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3 votes
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562 views

Platt Scaling vs Isotonic Regression

I am learning classifier probability calibrations and have calibrated an eleastic net model using both Platt scaling and isotonic regression. As you can see in the attached image Platt scaling (on the ...
yl637's user avatar
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2 votes
1 answer
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Are these any existing implementation of L1 isotonic regression in python?

An isotonic regression (https://en.wikipedia.org/wiki/Isotonic_regression) computes a fit (vector y_hat) which minimizes a specified loss to an observations vector y subject to isotonicity (non-...
Liran Katzir's user avatar
2 votes
0 answers
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Can isotonic regression be used as a discretisation scheme?

Working on two different projects, one involving isotonic regression, the other being about discretising continuous variables. I was wondering if there is a link between isotonic regression and ...
Lucas Morin's user avatar
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How to aggregate calibration curves which were created in cross validation?

When looking into Scikit's CalibratedClassifierCV I noticed that the object needs to keep multiple calibrated classifiers in memory to average the results in real time. I understand that these ...
sapo_cosmico's user avatar
11 votes
2 answers
807 views

How to test whether $\mu_1 < \mu_2 <\mu_3$?

Suppose I have three independent groups, with mean $\mu_1,~ \mu_2,~\mu_3$ respectively. How can I test whether $\mu_1 < \mu_2 <\mu_3$ or not using $n_1,~n_2,~n_3$ samples from each group? I ...
456 123's user avatar
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2 votes
1 answer
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Hypothesis test testing for monotonic group mean change

I wonder if there is a statistical hypothesis test testing whether group average monotonically increases across groups? For example, I have four treatment groups, A, B, C and D. I would like to test ...
WCMC's user avatar
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5 votes
1 answer
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What are drawbacks of isotonic regression?

I have been reading about isotonic regression and it seems like a great method that will give one a monotone regression function estimator and, moreover, is free of any tuning parameters. Why are ...
MerylStreep's user avatar
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1 answer
111 views

Seeking method for isotonic regression with bound constraints

I would like to fit an isotonic regression (with respect to "ordinary" linear ordering) to observations y_1, ..., y_n subject to the additional constraints that a <= y_1^* and y_10^* <= b where ...
Rolf Turner's user avatar
1 vote
0 answers
64 views

Multinomial classification where the response variable is monotonic over time

I have a set of feature and response variables measured for multiple subjects, each having multiple visit. Let's define $X_t^p$ as the feature variable at the $t^{th}$ observation of subject $p$, $...
oodalgic's user avatar
2 votes
1 answer
560 views

Estimate monotone function from noisy obsersations

Assume that $y=f(x)$ is an unknown monotonically increasing function of variable $x$. We have access to $N$ observations of this function given as tuples $(x_i,y_i)$, such that $y_i=f(x_i)$. The ...
dineshdileep's user avatar
2 votes
1 answer
3k views

recursive feature elimination: why select subset based on AUC vs sensitivity/specificity

I have a small dataset of 25 observations with a classification variable (factor 0,1) and 82 features scaled to have values between 0 and 1. I used the rfe() ...
Eric Green's user avatar
1 vote
2 answers
119 views

How can I refute a monotonic correlation

I have a binary target T and a continuous variable I expect to correlate with it. I expect some monotonic correlation, as the explaining variable increases I expect P(T) to increase. I collect some (...
Meir Maor's user avatar
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3 votes
1 answer
175 views

What's the correct method to rank populations?

I want to rank ten or so sources based on their respective error measurements. A few notes on the sources and measurements: The sources do not have the same number of measurements The number of ...
c00kiemonster's user avatar
1 vote
0 answers
138 views

Recalibrating a model predictions to incidence in coarse resolution, and measuring that its calibrated

I have a model that predicts a rare disease (1% prevalence) with good discrimination (AUC). However, the predictions it is giving can not be interpreted as probabilities. I want to recalibrate the ...
ihadanny's user avatar
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2 votes
3 answers
279 views

statistical test for two populations of proportions

I performed an experiment in which I measured the equilibration of a protein across two nuclei in a binucleated cell. This equilibration is expressed in percentages or proportions. I measured this for ...
mistakeNot's user avatar
2 votes
1 answer
54 views

Likelihood of Ordered Binomials

I have four numbers ($k_1 \dots k_4$) that come from 4 binomial trials with parameters $n$ and $\theta_1 \dots \theta_4$. I want to test (via likelihood ratio test) the hypotheses $$H_0: \theta_1 = \...
user avatar
2 votes
1 answer
2k views

Calibration after up and downsampling

I am experimenting with different techniques to deal with imbalanced classes in a classification problem. I am comparing upsampling the minority class with downsampling the majority class. Furthermore ...
Peter Lenaers's user avatar
1 vote
1 answer
2k views

Predicting the probability of product to be bought

I want to predict using statistical/machine-learning methods the probability of a person to buy a product on a website knowing the characteristics of the product and the other products it is compared ...
Pop's user avatar
  • 1,596
2 votes
1 answer
97 views

Multiplying SVM-derived probabilities with different levels of support

Let's assume there is a function of interest: y = abc ...where a, b, and c are the probabilities of independent events. I've created classification algorithms (specifically, SVMs) to estimate those ...
jda's user avatar
  • 131
1 vote
3 answers
265 views

Multiclass classification question

I am working on applying Random Forests to a multiclass classification problem, where I have a set of 11 predictor variables and a response that can take the values of "Yes", "No", and "Maybe". In my ...
Thomas Moore's user avatar
  • 1,695
1 vote
1 answer
333 views

Comparing and evaluating win probabilities in sports from different settings

Background I'm trying to predict the probability that the home teams wins a certain sports game, for each minute of the game. Taking these win probabilities together produces a nice visual of the ...
gieldops's user avatar
  • 111
2 votes
1 answer
509 views

Normalize logistics regression scores

I have four logistic regression model that predicts likelihood that customer make a purchase in 4 product categories(purchase event is rare and oversampled 50-50 for each model). Is there way to ...
Naveenan's user avatar
  • 173
1 vote
0 answers
822 views

Machine Learning: how do we usually select the best combination of parameters to obtain well-calibrated probabilities instead of classification task?

I have always dealt with Machine Learning problems involving classification tasks. I now have the following problem: obtain the purchasing probabilities of users given a certain dataset. Reading the ...
Pablo Fleurquin's user avatar
1 vote
1 answer
137 views

Testing for a non-zero, monotonic trend amongst 3 groups in a repeated-measures design

For each subject, we repeatedly measure 3 conditions for a scalar dependent variable. The research hypothesis is that there is a monotonic positive trend - that is, either 1<2<3 or 1=2<3 or 1&...
jona's user avatar
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5 votes
1 answer
655 views

Why bother looking at an omnibus ANOVA when I have a priori hypotheses about group differences?

I am examining three independent groups that were measured on a continuous outcome variable. I have a priori belief that the result should be Group 1 < Group 2 < Group 3. I've been told to do an ...
user1205901 - Слава Україні's user avatar
10 votes
2 answers
8k views

Is it right to consider the output of the neural network as its confidence in predicting the output?

Suppose I have a single output sigmoid (tanh) that is producing an output ranging [-1, +1]. Is it right to consider this output as its confidence measue of predicting the output. The output value ...
London guy's user avatar
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2 votes
1 answer
598 views

What does monotone polynomial plot represent?

I am trying to understand monotone and isotonic regression. I believe they will produce curve which are monotonely increasing or decreasing. In most of what I read on the net, the change is shown in a ...
rnso's user avatar
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3 votes
1 answer
4k views

Fit monotone polynomial to data

I want to fit monotone polynomials to data. Murray, Müller and Turlach (http://dx.doi.org/10.1007/s00180-012-0390-5) provide an implementation in R (http://cran.r-project.org/web/packages/MonoPoly/...
Somebody's user avatar
5 votes
1 answer
2k views

Applying isotonic regression calibration (using PAV) to new model predictions

I'm working on classifying models for a few different projects. Several papers on the subject of calibration all suggest using isotonic regression (using PAV) to adjust the model probabilities. I ...
user21067's user avatar
3 votes
1 answer
2k views

Chi-Square test: one-sided implementation?

I need to compare two samples and I would like to know if the distribution of the first stochastically dominates that of the second one. I'm not sure whether with the Chi-Square test I can verify ...
Ricky Robinson's user avatar
12 votes
2 answers
31k views

Is it "okay" to plot a regression line for ranked data (Spearman correlation)?

I have data for which I calculated the Spearman correlation and want to visualize it for a publication. The dependent variable is ranked, the independet variable is not. What I want to visualize is ...
Sentry's user avatar
  • 602
2 votes
1 answer
98 views

Would multiple t-tests be appropriate

I have reaction time data from four different age groups, and I am hoping to prove that reaction time improves with age. I know that ANOVA would be preferred to determine if age has an effect, but I ...
kdk's user avatar
  • 43
7 votes
1 answer
3k views

why is adaboost predicting probabilities with so little standard deviation?

I'm using several algorithms to predict a binary target. So far I tried Gradient Boosting, Random Forest, Extra Random Trees and adaboost from scikit learn. All of these algorithms appear to predict ...
ADJ's user avatar
  • 435
1 vote
2 answers
732 views

Convert linear SVM answers to class probability?

How to do this? I use SVMlight that returns me some scores (which say how sure SVM is that something belongs to a class?) The questions is - can I do something to convert it to a % probability? Any ...
user3010273's user avatar
2 votes
1 answer
2k views

Nonparametric test for trend using Python

I am looking to perform a nonparametric test for trend on a continuous outcome across three groups, preferably in Python. For example height (pretend height is not normal) in 4th, 5th and 6th graders....
alexhli's user avatar
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3 votes
0 answers
2k views

Estimators for linear regression when multicollinearity is present [closed]

I have a multicollinearity problem in a linear regression model and ridge regression was suggested as a solution. So I have spent quite some time researching different ridge regressors in the ...
Baz's user avatar
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4 votes
1 answer
2k views

1D weighted Isotonic Regression (PAV): a simple description of the algorithm

I have to use IsotonicRegression class from scikit-learn with non-uniform point weights: in method IsotonicRegression.fit parameter ...
Felix's user avatar
  • 285
1 vote
2 answers
197 views

One-way table largest proportion test

Suppose I've a one-way table with three categories (A, B and C), and let $p_a$, $p_b$ and $p_c$ be the true proportion of observations in each category, i.e. $p_a+p_b+p_c=1$. How can I conduct a ...
David L's user avatar
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