# 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 ...
• 4,377
1 vote
119 views

### 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 ...
• 11
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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 ...
• 113
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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 ...
• 1,826
1 vote
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 ...
1 vote
18 views

### 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 ...
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 ...
1 vote
1k views

### 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),...
• 616
1 vote
140 views

### 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 $y_1,y_2, \dots y_m$, ...
• 33
1 vote
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 ...
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4k views

### 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 ...
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718 views

### 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 ...
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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 ...
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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-...
94 views

### 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 ...
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213 views

### 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 ...
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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 ...
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268 views

### 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 ...
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1k views

### 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 ...
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