arXiv subjects

Ingrid Hobæk Haff

Publications and source records attributed to Ingrid Hobæk Haff.

9 recordsLinked to original sources

arXiv2026

The asymptotic effect of tuning parameters

Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the balance parameter in hybrid methods. Typically tuning parameters are set to the minimizers of some estimator of the risk, a step which introduces additional randomness and makes standard methodology inapplicable. We derive precise asymptotic theory for this situation. Our framework allows for smooth, but otherwise arbitrary, loss functions and for the risk to be estimated by cross-validation procedures. Results include consistency of the optimal estimator towards a well-defined quantity and asymptotic normality after proper scaling and centring. We give explicit forms and estimators for the limiting variance matrix and results sharply characterizing the distance from the training error to the cross-validated estimator of the risk.

math.ST↗

arXiv2026

Stepwise Variational Inference with Vine Copulas

We propose stepwise variational inference (VI) with vine copulas: a universal VI procedure that combines vine copulas with a novel stepwise estimation procedure of the variational parameters. Vine copulas consist of a nested sequence of trees built from copulas, where more complex latent dependence can be modeled with increasing number of trees. We propose to estimate the vine copula approximate posterior in a stepwise fashion, tree by tree along the vine structure. Further, we show that the usual backward Kullback-Leibler divergence cannot recover the correct parameters in the vine copula model, thus the evidence lower bound is defined based on the Rényi divergence. Finally, an intuitive stopping criterion for adding further trees to the vine eliminates the need to pre-define a complexity parameter of the variational distribution, as required for most other approaches. Thus, our method interpolates between mean-field VI (MFVI) and full latent dependence. In many applications, in particular sparse Gaussian processes, our method is parsimonious with parameters, while outperforming MFVI.

stat.ML↗

arXiv2025

TVineSynth: A Truncated C-Vine Copula Generator of Synthetic Tabular Data to Balance Privacy and Utility

We propose TVineSynth, a vine copula based synthetic tabular data generator, which is designed to balance privacy and utility, using the vine tree structure and its truncation to do the trade-off. Contrary to synthetic data generators that achieve DP by globally adding noise, TVineSynth performs a controlled approximation of the estimated data generating distribution, so that it does not suffer from poor utility of the resulting synthetic data for downstream prediction tasks. TVineSynth introduces a targeted bias into the vine copula model that, combined with the specific tree structure of the vine, causes the model to zero out privacy-leaking dependencies while relying on those that are beneficial for utility. Privacy is here measured with membership (MIA) and attribute inference attacks (AIA). Further, we theoretically justify how the construction of TVineSynth ensures AIA privacy under a natural privacy measure for continuous sensitive attributes. When compared to competitor models, with and without DP, on simulated and on real-world data, TVineSynth achieves a superior privacy-utility balance.

cs.LG↗

arXiv2024

Boosting with copula-based components

The authors propose new additive models for binary outcomes, where the components are copula-based regression models (Noh et al, 2013), and designed such that the model may capture potentially complex interaction effects. The models do not require discretisation of continuous covariates, and are therefore suitable for problems with many such covariates. A fitting algorithm, and efficient procedures for model selection and evaluation of the components are described. Software is provided in the R-package copulaboost. Simulations and illustrations on data sets indicate that the method's predictive performance is either better than or comparable to the other methods.

stat.ME↗

arXiv2024

Generalised logistic regression with vine copulas

We propose a generalisation of the logistic regression model, that aims to account for non-linear main effects and complex interactions, while keeping the model inherently explainable. This is obtained by starting with log-odds that are linear in the covariates, and adding non-linear terms that depend on at least two covariates. More specifically, we use a generative specification of the model, consisting of a combination of certain margins on natural exponential form, combined with vine copulas. The estimation of the model is however based on the discriminative likelihood, and dependencies between covariates are included in the model, only if they contribute significantly to the distinction between the two classes. Further, a scheme for model selection and estimation is presented. The methods described in this paper are implemented in the R package LogisticCopula. In order to assess the performance of our model, we ran an extensive simulation study. The results from the study, as well as from a couple of examples on real data, showed that our model performs at least as well as natural competitors, especially in the presence of non-linearities and complex interactions, even when $n$ is not large compared to $p$.

stat.ME↗

arXiv2021

The fraud loss for selecting the model complexity in fraud detection

In fraud detection applications, the investigator is typically limited to controlling a restricted number k of cases. The most efficient manner of allocating the resources is then to try selecting the k cases with the highest probability of being fraudulent. The prediction model used for this purpose must normally be regularized to avoid overfitting and consequently bad prediction performance. A new loss function, denoted the fraud loss, is proposed for selecting the model complexity via a tuning parameter. A simulation study is performed to find the optimal settings for validation. Further, the performance of the proposed procedure is compared to the most relevant competing procedure, based on the area under the receiver operating characteristic curve (AUC), in a set of simulations, as well as on a VAT fraud dataset. In most cases, choosing the complexity of the model according to the fraud loss, gave a better than, or comparable performance to the AUC in terms of the fraud loss.

stat.AP↗

arXiv2019

Modelling extreme claims via composite models and threshold selection methods

The existence of large and extreme claims of a non-life insurance portfolio influences the ability of (re)insurers to estimate the reserve. The excess over-threshold method provides a way to capture and model the typical behaviour of insurance claim data. This paper discusses several composite models with commonly used bulk distributions, combined with a 2-parameter Pareto distribution above the threshold. We have explored how several threshold selection methods perform when estimating the reserve as well as the effect of the choice of bulk distribution, with varying sample size and tail properties. To investigate this, a simulation study has been performed. Our study shows that when data are sufficient, the square root rule has the overall best performance in terms of the quality of the reserve estimate. The second best is the exponentiality test, especially when the right tail of the data is extreme. As the sample size becomes small, the simultaneous estimation has the best performance. Further, the influence of the choice of bulk distribution seems to be rather large, especially when the distribution is heavy-tailed. Moreover, it shows that the empirical estimate of $p_{\leq b}$, the probability that a claim is below the threshold, is more robust than the theoretical one.

stat.AP↗

arXiv2018

One family, six distributions -- A flexible model for insurance claim severity

We propose a new class of claim severity distributions with six parameters, that has the standard two-parameter distributions, the log-normal, the log-Gamma, the Weibull, the Gamma and the Pareto, as special cases. This distribution is much more flexible than its special cases, and therefore more able to to capture important characteristics of claim severity data. Further, we have investigated how increased parameter uncertainty due to a larger number of parameters affects the estimate of the reserve. This is done in a large simulation study, where both the characteristics of the claim size distributions and the sample size are varied. We have also tried our model on a set of motor insurance claims from a Norwegian insurance company. The results from the study show that as long as the amount of data is reasonable, the five- and six-parameter versions of our model provide very good estimates of both the quantiles of the claim severity distribution and the reserves, for claim size distributions ranging from medium to very heavy tailed. However, when the sample size is small, our model appears to struggle with heavy-tailed data, but is still adequate for data with more moderate tails.

stat.ME↗

arXiv2013

Parameter estimation for pair-copula constructions

We explore various estimators for the parameters of a pair-copula construction (PCC), among those the stepwise semiparametric (SSP) estimator, designed for this dependence structure. We present its asymptotic properties, as well as the estimation algorithm for the two most common types of PCCs. Compared to the considered alternatives, that is, maximum likelihood, inference functions for margins and semiparametric estimation, SSP is in general asymptotically less efficient. As we show in a few examples, this loss of efficiency may however be rather low. Furthermore, SSP is semiparametrically efficient for the Gaussian copula. More importantly, it is computationally tractable even in high dimensions, as opposed to its competitors. In any case, SSP may provide start values, required by the other estimators. It is also well suited for selecting the pair-copulae of a PCC for a given data set.

math.ST↗