# Tag Info

49

To add a visual explanation to this: let's consider a few points that you plan to model. They look like they could be described well with a straight line, so you fit a linear regression to them: This regression line lets you both interpolate (generate expected values in between your data points) and extrapolate (generate expected values outside the range ...

20

In essence interpolation is an operation within the data support, or between existing known data points; extrapolation is beyond the data support. Otherwise put, the criterion is: where are the missing values? One reason for the distinction is that extrapolation is usually more difficult to do well, and even dangerous, statistically if not practically. ...

12

You are right to be concerned - even the best models can fail spectacularly if the distribution of out-of-sample data differs significantly from the distribution of the data that the model was trained/tested on. I think the best you can do is train a model on the labelled data that you have, but try to keep the model interpretable. That probably means only ...

12

TL;DR version: Interpolation takes place between existing data points. Extrapolation takes place beyond them. Mnemonic: interpolation => inside. FWIW: The prefix inter- means between, and extra- means beyond. Think also of interstate highways which go between states, or extraterrestrials from beyond our planet.

7

The typical approach to this problem is land-use regression (LUR). LUR hybridize methods for correlated data analysis and spatiotemporal dependence structures. Typically, at each site, there are one or more covariates which can be predicted at each geographic location, like proximity to highway, season, time of day, elevation, or other features. It's ...

4

I'm not sure I entirely understand that question, but so far as I understand it you're asking how to train a classifier to predict on samples lying outside the domain of the samples it has already seen. This is, generally speaking and so far as I know, not possible. Machine learning theory is based on the idea of "empirical risk minimization," which boils ...

3

Recall two facts: Number of eigenvalues is equal to rank of matrix. Sum of eigenvalues of matrix is equal to it's trace (sum of entries on diagonal). In PCA "matrix" mentioned above is correlation or covariance matrix of your data set, so (provided none of your variables is linear combination of others): Number of eigenvalues is equal to number of ...

2

This is tantamount to asking whether, if you knew $x + y = 20$, can you identify $x$ and $y$ uniquely. The answer is, of course, no. There are infinitely many possible solutions.

2

Some assumptions need to be made to extrapolate (far) beyond the range of the data you have. These assumptions could either be parametric models or something like repeating the hazard of the last year (or last 2 years) over and over. The latter approach is quite a strong assumption (more or less extrapolation with an exponential distribution based on the ...

2

You can use the predict function. Try: set.seed(123) x <- 1:10 y <- -2 + 3 * x + rnorm(10) our_data <- data.frame(y = y, x = x) our_model <- lm(y ~ x, data = our_data) predict(our_model, newdata = data.frame(x = 20))

2

From a practical standpoint it is difficult/unreasonable to ask a model to predict something on cases that are not possible in the current system (no free lunch). One way to circumvent that problem is to add randomization to the current (deployed) system, e.g. to add the possibility to bypass (some of) the rules with a small, controlled probability (and ...

2

One thing that has worked for us in a similar situation is doing a bit of reinforcement learning (explore and exploit). On top of the rule based model, we ran a explorer which would with a small likelihood change the response of the model, so in occasional cases where the model would not recommend a card to a 17-year old, the explorer would overturn the ...

2

The model you defined above looks like this (where GDP growth is $G_t$ and spread is $S_t$): $$G_t = a + bS_t + \varepsilon_t$$ It is a conditional model of $G_t$, given $S_t$. If you have a value of $S_t$ for a given $t$ as input, it will output an estimate of $G_t$ for that same date (the mean of $G_t$ conditional on $S_t$, for example). This means that ...

2

Must eigenvalues converge to zero at higher dimensions? Or is it possible for eigenvalues to converge at a finite value? For any matrix of finite dimensions, it has a finite number of eigenvalues. Every finite sequence converges to the final value of the sequence. Consider this definition of convergence of a sequence: A sequence $x_n$ is said to be ...

2

Your rules may give you a way to perform data augmentation. Copy a positive sample, change the age to 17, and then mark it as a negative sample. This procedure won't necessarily be trivial or useful for all datasets. I work with NLP data and it's tricky to do well in that domain. For example, if you have other features correlated with age, you may end up ...

1

Example: Study: Want to fit a simple linear regression on the height on the age for girls of age 6-15 years old. Sample size is 100, age is calculated by (date of measuring - date of birth)/365.25. After data collection, model is fit and get the estimate of intercept b0 and slope b1. it means we have E(height|age) = b0 + b1*age. When you want the mean ...

1

Based on the analysis you did, the claim is indeed about individual behavior. In your example, you are interested in the probability of being in B1 vs. B2 for an individual in A1. For that individual, their outcome of B1 or B2 is governed by a parameter that applies to them (it may apply to others as well, but the focus here is on the individual). You are ...

1

That is exactly what an statistical test is for, but, you must make sure that your sample of 30 individuals has the power to test your hypothesis. The best is to perform an a-priori power analysis, before you sample 30 individuals. Otherwise, how did you decided 30 was enough? It would also depend on the size of the population you are sampling from, if ...

1

There are clearly two different segments to each curve. I suggest fitting each separately. While it is heating up, it looks exponential - see whether log(250-t) is linear. While it is cooling down, it looks quadratic, so I suggest seeing whether sqrt(t-75) is linear.

1

The shape of the eigenvalue plot is entirely determined by your underlying data generating process and will only follow a smooth trend if the underlying processes have a smooth distribution of contributing to the variation. This would be quite possible in a real world observation study, but would be unlikely in an experiment where some conditions are well ...

1

The classical statistical answer is that if the selection process is in the data and described by the model or selection is at random then the parametrical model contemplates it correctly. See Donald Rubin paper Inference and Missing data (1976). You do need to include the mechanism of data selection in your model. This is a field where parametric inference ...

1

If you apply the same assumed model (meagre analysis) you are imposing a specification. Time series analysis listens to the data , challenges unusual values , detects nuances and separates the observations to signal (fitted values) and noise . The signal is then extrapolated and forecast confidence limits are generated based possible reoccurring of anomalies....

1

What you are doing is forecasting. Judging from what you write in the comments, forecasting this series is not truly a statistical problem, but a biological one. Best to model the dynamics giving rise to this curve and then extrapolate these out. From a purely statistical/forecasting standpoint, the best you can probably do is the so-called naive or random-...

1

Old Ans. The Y data takes negative values. You could try fitting $Y+11.0$ or more generally $Y+Y_{min}$ with a gamma distribution which may also need an offset. Without more information, it is guesswork. Either show tabular data or forget getting a good answer, not clear enough. After comments, edits and more information. OK, you can try a less than ...

1

This is akin to the after-life dilemma: what ratio of good and bad deeds (data) is sufficient to get to heaven instead of hell (class), after one dies (filter!). Herein, death serves as the filter, leading to missing values towards a supervised learning scheme. I want to disambiguate between missing-value problem and 'biased data' problem. There is no such ...

1

You can smooth without strong assumptions on the functional form of the relationship (you need to assume the relationship is smooth and not too rapidly-varying). The data may go up a little, or up a lot, or stay fairly flat or go down, or oscillate, and a smoother can follow it -- smoothing methods achieve this by being adaptive enough to fit the main trend ...

1

Once your model and its parameters are fixed, there's only one way to do it: plug in the covariate values of the point you want to extrapolate at.

1

If RevMan is computing the mean difference internally then it may be that you can supply any two means which have the required mean difference. Try it and see. More specifically if the mean difference you have is 10 then run it with 0 and 10 and then again with 990 and 1000. If RevMan gives you the same answer then you are in clover.

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