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Danijel Kivaranovic

Publications and source records attributed to Danijel Kivaranovic.

6 recordsLinked to original sources
arXiv2024

A (tight) upper bound for the length of confidence intervals with conditional coverage

We show that two popular selective inference procedures, namely data carving (Fithian et al., 2017) and selection with a randomized response (Tian et al., 2018b), when combined with the polyhedral method (Lee et al., 2016), result in confidence intervals whose length is bounded. This contrasts results for confidence intervals based on the polyhedral method alone, whose expected length is typically infinite (Kivaranovic and Leeb, 2020). Moreover, we show that these two procedures always dominate corresponding sample-splitting methods in terms of interval length.

stat.ME↗
arXiv2020

Conformal prediction intervals for the individual treatment effect

We propose several prediction intervals procedures for the individual treatment effect with either finite-sample or asymptotic coverage guarantee in a non-parametric regression setting, where non-linear regression functions, heteroskedasticity and non-Gaussianity are allowed. The construct the prediction intervals we use the conformal method of Vovk et al. (2005). In extensive simulations, we compare the coverage probability and interval length of our prediction interval procedures. We demonstrate that complex learning algorithms, such as neural networks, can lead to narrower prediction intervals than simple algorithms, such as linear regression, if the sample size is large enough.

stat.ME↗
arXiv2020

Adaptive, Distribution-Free Prediction Intervals for Deep Networks

The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees. We present methods from the statistics literature that can be used efficiently with neural networks under minimal assumptions with guaranteed performance. We propose a neural network that outputs three values instead of a single point estimate and optimizes a loss function motivated by the standard quantile regression loss. We provide two prediction interval methods with finite sample coverage guarantees solely under the assumption that the observations are independent and identically distributed. The first method leverages the conformal inference framework and provides average coverage. The second method provides a new, stronger guarantee by conditioning on the observed data. Lastly, our loss function does not compromise the predictive accuracy of the network like other prediction interval methods. We demonstrate the ease of use of our procedures as well as its improvements over other methods on both simulated and real data. As most deep networks can easily be modified by our method to output predictions with valid prediction intervals, its use should become standard practice, much like reporting standard errors along with mean estimates.

stat.ML↗
arXiv2019

On the length of post-model-selection confidence intervals conditional on polyhedral constraints

Valid inference after model selection is currently a very active area of research. The polyhedral method, pioneered by Lee, et al. (2016), allows for valid inference after model selection if the model selection event can be described by polyhedral constraints. In that reference, the method is exemplified by constructing two valid confidence intervals when the Lasso estimator is used to select a model. We here study the length of these intervals. For one of these confidence intervals, which is easier to compute, we find that its expected length is always infinite. For the other of these confidence intervals, whose computation is more demanding, we give a necessary and sufficient condition for its expected length to be infinite. In simulations, we find that this sufficient condition is typically satisfied, unless the selected model includes almost all or almost none of the available regressors. For the distribution of confidence interval length, we find that the $κ$-quantiles behave like $1/(1-κ)$ for $κ$ close to $1$. Our results can also be used to analyze other confidence intervals that are based on the polyhedral method.

math.ST↗
arXiv2019

The Oracle of DLphi

We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results. Having access to a sufficiently large amount of labelled training data, our methodology is capable of predicting the labels of the test data almost always even if the training data is entirely unrelated to the test data. In other words, we prove in a specific setting that as long as one has access to enough data points, the quality of the data is irrelevant.

cs.LG↗