Academic interests
- Multivariate statistics, and copulae in particular
- Skew and heavy-tailed distributions
- Applications within insurance and finance
Courses taught
STK4520 - Laboratory for Finance and Insurance Mathematics
Background
I finished my master's degree in industrial mathematics at NTNU in 2002. Then I started working at the Norwegian Computing Centre, first as a research scientist and later as a senior research scientist. From 2008 to 2012, I was a PhD student at the centre Statistics for Innovation, with a 20% position as a research scientist at the Norwegian Computing Centre. Since 2015 I am Associate professor in insurance mathematics and statistics at the Department of mathematics at the University of Oslo.
Awards
The Sverdrup award for young scientists
The mathematical award of Hanna og John Olav Stubban
Partners
The Norwegian Computing Centre
Tags:
statistics and data science
Publications
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Haff, Ingrid Hobæk; Huseby, Arne Bang & Wang, Yinzhi
(2026).
Optimal reinsurance for several lines of business.
Scandinavian Actuarial Journal.
ISSN 0346-1238.
doi:
10.1080/03461238.2026.2650318.
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Actuarial literature contains countless formulations and analytical results of optimal reinsurance for a single risk, but there is limited research on optimal solutions when the cedent runs many lines of business and is asked to manage the total risk in a certain integrated sense. In this paper, we extend the problem of optimal reinsurance to a multivariate framework where the cedent has multiple risks that cannot be bundled together into one. More specifically, we optimize layer contracts using a more industrially based criterion, where risk and profit are balanced through a ratio between the value-at-risk and the expected surplus. The effects of the marginal risk distributions and the dependence structure, as well as of the premium principle, are investigated. Using convexity theory, we show that the optimal solution is strongly related to the monotonicity property of the hazard rate functions of the risks. For decreasing hazard rates the solution can typically be found by Lagrangian optimization, while for increasing hazard rates, one often ends up with an extreme point solution, where at least one of the contracts is a stop-loss one. Further, the joint optimization of the contracts results in a better balance between risk and expected gain than when the contracts are optimized separately, even when the risks are independent. This advantage increases with the dependence between the risks, as well as when the marginal risk distributions become more heavy-tailed.
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Brant, Simon Boge & Haff, Ingrid Hobæk
(2026).
Boosting with copula-based components.
Statistics and computing.
ISSN 0960-3174.
36(2).
doi:
10.1007/s11222-025-10815-3.
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We propose new additive boosting models, 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 discretization of continuous covariates, and are therefore suitable for problems with many such covariates. We propose a fitting algorithm based on efficient procedures for model selection and evaluation of model components, which might be used for designing more effective model selection and fitting algorithms for other types of copula based regression models. Software is provided in the R-package copulaboost. Through a simulation study and illustrations on data, we show that the method’s predictive performance is either better than or comparable to the other equivalent methods.
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Riccardi, Enrico; Minotto, Thomas; Haff, Ingrid Hobæk & Sandve, Geir Kjetil Ferkingstad
(2025).
Connecting instance and model sparsity in multiple instance learning.
Machine Learning with Applications (MLWA).
21,
p. 100679–100679.
doi:
10.1016/j.mlwa.2025.100679.
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Minotto, Thomas; Haff, Ingrid Hobæk; Riccardi, Enrico & Sandve, Geir Kjetil Ferkingstad
(2025).
Detecting statistical interactions in immune receptor data: a comparative study.
Journal of Applied Statistics.
ISSN 0266-4763.
p. 22–22.
doi:
10.1080/02664763.2025.2533483.
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Griesbauer, Elisabeth Maria; Czado, Claudia; Frigessi, Arnoldo & Haff, Ingrid Hobæk
(2025).
TVineSynth: A Truncated C-Vine Copula Generator of Synthetic Tabular Data to Balance Privacy and Utility.
Proceedings of Machine Learning Research (PMLR).
258,
p. 3511–3519.
doi:
https:/raw.githubusercontent.com/mlresearch/v258/main/assets/griesbauer25a/griesbauer25a.pdf.
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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.
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Chernigovskaia, Maria; Pavlović, Milena; Kanduri, Chakravarthi; Gielis, Sofie; Robert, Philippe & Scheffer, Lonneke
[Show all 12 contributors for this article]
(2025).
Simulation of adaptive immune receptors and repertoires with complex immune information to guide the development and benchmarking of AIRR machine learning.
Nucleic Acids Research (NAR).
ISSN 0305-1048.
53(3).
doi:
10.1093/nar/gkaf025.
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Machine learning (ML) has shown great potential in the adaptive immune receptor repertoire (AIRR) field. However, there is a lack of large-scale ground-truth experimental AIRR data suitable for AIRR-ML-based disease diagnostics and therapeutics discovery. Simulated ground-truth AIRR data are required to complement the development and benchmarking of robust and interpretable AIRR-ML methods where experimental data is currently inaccessible or insufficient. The challenge for simulated data to be useful is incorporating key features observed in experimental repertoires. These features, such as antigen or disease-associated immune information, cause AIRR-ML problems to be challenging. Here, we introduce LIgO, a software suite, which simulates AIRR data for the development and benchmarking of AIRR-ML methods. LIgO incorporates different types of immune information both on the receptor and the repertoire level and preserves native-like generation probability distribution. Additionally, LIgO assists users in determining the computational feasibility of their simulations. We show two examples where LIgO supports the development and validation of AIRR-ML methods: (i) how individuals carrying out-of-distribution immune information impacts receptor-level prediction performance and (ii) how immune information co-occurring in the same AIRs impacts the performance of conventional receptor-level encoding and repertoire-level classification approaches. LIgO guides the advancement and assessment of interpretable AIRR-ML methods.
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O'Donnell, Timothy J.; Kanduri, Chakravarthi; Isacchini, Giulio; Limenitakis, Julien P.; Brachman, Rebecca A. & Alvarez, Raymond A.
[Show all 9 contributors for this article]
(2024).
Reading the repertoire: Progress in adaptive immune receptor analysis using machine learning.
Cell Systems.
ISSN 2405-4712.
15(12),
p. 1168–1189.
doi:
10.1016/j.cels.2024.11.006.
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The adaptive immune system holds invaluable information on past and present immune responses in the form of B and T cell receptor sequences, but we are limited in our ability to decode this information. Machine learning approaches are under active investigation for a range of tasks relevant to understanding and manipulating the adaptive immune receptor repertoire, including matching receptors to the antigens they bind, generating antibodies or T cell receptors for use as therapeutics, and diagnosing disease based on patient repertoires. Progress on these tasks has the potential to substantially improve the development of vaccines, therapeutics, and diagnostics, as well as advance our understanding of fundamental immunological principles. We outline key challenges for the field, highlighting the need for software benchmarking, targeted large-scale data generation, and coordinated research efforts.
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Minotto, Thomas; Robert, Philippe; Haff, Ingrid Hobæk & Sandve, Geir Kjetil Ferkingstad
(2024).
Assessing the feasibility of statistical inference using synthetic antibody-antigen datasets.
Statistical Applications in Genetics and Molecular Biology.
23:20230027(1),
p. 1–14.
doi:
10.1515/sagmb-2023-0027.
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Simulation frameworks are useful to stress-test predictive models when data is scarce, or to assert model sensitivity to specific data distributions. Such frameworks often need to recapitulate several layers of data complexity, including emergent properties that arise implicitly from the interaction between simulation components. Antibody-antigen binding is a complex mechanism by which an antibody sequence wraps itself around an antigen with high affinity. In this study, we use a synthetic simulation framework for antibody-antigen folding and binding on a 3D lattice that include full details on the spatial conformation of both molecules. We investigate how emergent properties arise in this framework, in particular the physical proximity of amino acids, their presence on the binding interface, or the binding status of a sequence, and relate that to the individual and pairwise contributions of amino acids in statistical models for binding prediction. We show that weights learnt from a simple logistic regression model align with some but not all features of amino acids involved in the binding, and that predictive sequence binding patterns can be enriched. In particular, main effects correlated with the capacity of a sequence to bind any antigen, while statistical interactions were related to sequence specificity.
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Bølviken, Erik Helmer & Haff, Ingrid Hobæk
(2024).
Loss modeling with many-parameter distributions.
Scandinavian Actuarial Journal.
ISSN 0346-1238.
2024(8),
p. 763–780.
doi:
10.1080/03461238.2024.2309987.
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It is argued that many-parameter families of loss distributions may work even with limited amounts of historical data. A restriction to unimodality works as a stabilizer, which makes fitted distributions much more stable than their parameters. We propose Box-Cox transformed Gamma and Burr variables. Those are models with three or four parameters with many of the traditional two-parameter families as special cases, and there are well-defined distributions at the boundaries of the parameter space, which is important for stability. The approach is evaluated with model error defined though the theory of misspecification in statistics. It is shown that such error is drastically reduced when a third or fourth parameter is added without increasing the random error more than a little. It is pointed out that the approach may be a suitable starting point for completely automatic procedures.
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Scheffer, Lonneke; Reber, Eric Emanuel; Mehta, Brij Bhushan; Pavlović, Milena; Chernigovskaia, Maria & Richardson, Eve
[Show all 11 contributors for this article]
(2024).
Predictability of antigen binding based on short motifs in the antibody CDRH3.
Briefings in Bioinformatics.
ISSN 1467-5463.
25(6),
p. 1–10.
doi:
10.1093/bib/bbae537.
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Adaptive immune receptors, such as antibodies and T-cell receptors, recognize foreign threats with exquisite specificity. A major challenge in adaptive immunology is discovering the rules governing immune receptor–antigen binding in order to predict the antigen binding status of previously unseen immune receptors. Many studies assume that the antigen binding status of an immune receptor may be determined by the presence of a short motif in the complementarity determining region 3 (CDR3), disregarding other amino acids. To test this assumption, we present a method to discover short motifs which show high precision in predicting antigen binding and generalize well to unseen simulated and experimental data. Our analysis of a mutagenesis-based antibody dataset reveals 11 336 position-specific, mostly gapped motifs of 3–5 amino acids that retain high precision on independently generated experimental data. Using a subset of only 178 motifs, a simple classifier was made that on the independently generated dataset outperformed a deep learning model proposed specifically for such datasets. In conclusion, our findings support the notion that for some antibodies, antigen binding may be largely determined by a short CDR3 motif. As more experimental data emerge, our methodology could serve as a foundation for in-depth investigations into antigen binding signals.
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Dæhlen, Ingrid; Hjort, Nils Lid & Haff, Ingrid Hobæk
(2023).
Accurate bias estimation with applications to focused model selection.
Scandinavian Journal of Statistics.
ISSN 0303-6898.
p. 1–36.
doi:
10.1111/sjos.12696.
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Abstract We derive approximations to the bias and squared bias with errors of order where is the sample size. Our results hold for a large class of estimators, including quantiles, transformations of unbiased estimators, maximum likelihood estimators in (possibly) incorrectly specified models, and functions thereof. Furthermore, we use the approximations to derive estimators of the mean squared error (MSE) which are correct to order . Since the variance of many estimators is of order , this level of precision is needed for the MSE estimator to properly take the variance into account. We also formulate a new focused information criterion (FIC) for model selection based on the estimators of the squared bias. Lastly, we illustrate the methods on data containing the number of battle deaths in all major inter‐state wars between 1823 and the present day. The application illustrates the potentially large impact of using a less‐accurate estimator of the squared bias.
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Bakka, Haakon Christopher; Rognebakke, Hanne Therese Wist; Glad, Ingrid Kristine; Haff, Ingrid Hobæk & Vanem, Erik
(2022).
Estimating the effect of biofouling on ship shaft power based on sensor measurements.
Ship Technology Research.
ISSN 0937-7255.
70(3),
p. 209–221.
doi:
10.1080/09377255.2022.2159108.
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Marine biofouling on a ship's hull and propeller increases the resistance of the ship moving through water and reduces the propulsion efficiency of the ship. Estimating the effect of fouling is difficult, as the biomass is rarely measured. In this paper, we present a new data-driven model for the total shaft power use of a large containership, in order to estimate the unobserved effect of fouling. Due to the limitations of both physical models and machine learning models, we develop a Bayesian generalized additive model for our purpose. We discuss issues of representative training data for the model. Further, we subset and subsample the data to a representative sample. Models are compared by out-of-sample predictive quality, physical appropriateness, and through autocorrelation of residuals. The Bayesian generalized additive model combined with computational inference using integrated nested Laplace approximations gives a robust estimate of the biofouling effect over time. It also allows a decomposition of the total shaft power use into effects of speed, weather, and other conditions. This model can be used to understand the effectiveness and timing of different hull and propeller treatments.
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Brant, Simon Boge & Haff, Ingrid Hobæk
(2022).
The fraud loss for selecting the model complexity in fraud detection.
Journal of Applied Statistics.
ISSN 0266-4763.
doi:
10.1080/02664763.2022.2070137.
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Statistical fraud detection consists in making a system that automatically selects a subset of all cases (insurance claims, financial transactions, etc.) that are the most interesting for further investigation. The reason why such a system is needed is that the total number of cases typically is much higher than one realistically could investigate manually and that fraud tends to be quite rare. Further, the investigator is typically limited to controlling a restricted number k of cases, due to limited resources. The most efficient manner of allocating these 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 regularised to avoid overfitting and consequently bad prediction performance. A 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 credit card default dataset. Choosing the complexity of the model by the fraud loss resulted in either comparable or better results in terms of the fraud loss than choosing it according to the AUC.
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Minotto, Thomas; Haff, Ingrid Hobæk & Sandve, Geir Kjetil Ferkingstad
(2022).
Detecting statistical interactions in immune receptor datasets.
In Torelli, Nicola; BELLIO, RUGGERO & MUGGEO, VITO (Ed.),
Proceedings of the 36th International Workshop on Statistical Modelling.
EUT Edizioni Università di Trieste.
ISSN 9788855113090.
p. 253–257.
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Recent progress in the understanding of immune receptors suggests that complex interactions between amino acids are important in determining binding to antigens. Yet, current methods focus mostly on constructing good predictors for the data with complex models, and less on the understanding of the underlying interaction effects. Here, we attempt to retrieve high-order statistical interactions in immune receptor data with different methods. We study performance at this task in a large simulation study, and how it depends on the order, amount and strength of the interactions, witness rate and sample size. The results show that pairwise interactions are easily retrieved, but model complexity harms detection. Interactions are better detected in larger samples, but the process is then slower.
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Akbar, Rahmad; Robert, Philippe Paul Auguste; Weber, Cédric R.; Widrich, Michael; Frank, Robert & Pavlovic, Milena
[Show all 19 contributors for this article]
(2022).
In silico proof of principle of machine learning-based antibody design at unconstrained scale.
mAbs.
ISSN 1942-0862.
14:e2031482(1),
p. 1–18.
doi:
10.1080/19420862.2022.2031482.
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Generative machine learning (ML) has been postulated to become a major driver in the computational design of antigen-specific monoclonal antibodies (mAb). However, efforts to confirm this hypothesis have been hindered by the infeasibility of testing arbitrarily large numbers of antibody sequences for their most critical design parameters: paratope, epitope, affinity, and developability. To address this challenge, we leveraged a lattice-based antibody-antigen binding simulation framework, which incorporates a wide range of physiological antibody-binding parameters. The simulation framework enables the computation of synthetic antibody-antigen 3D-structures, and it functions as an oracle for unrestricted prospective evaluation and benchmarking of antibody design parameters of ML-generated antibody sequences. We found that a deep generative model, trained exclusively on antibody sequence (one dimensional: 1D) data can be used to design conformational (three dimensional: 3D) epitope-specific antibodies, matching, or exceeding the training dataset in affinity and developability parameter value variety. Furthermore, we established a lower threshold of sequence diversity necessary for high-accuracy generative antibody ML and demonstrated that this lower threshold also holds on experimental real-world data. Finally, we show that transfer learning enables the generation of high-affinity antibody sequences from low-N training data. Our work establishes a priori feasibility and the theoretical foundation of high-throughput ML-based mAb design.
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Slabodkin, Andrei; Chernigovskaia, Maria; Mikocziova, Ivana; Akbar, Rahmad; Scheffer, Lonneke & Pavlović, Milena
[Show all 16 contributors for this article]
(2021).
Individualized VDJ recombination predisposes the available Ig sequence space.
Genome Research.
ISSN 1088-9051.
31(12),
p. 2209–2225.
doi:
10.1101/gr.275373.121.
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The process of recombination between variable (V), diversity (D), and joining (J) immunoglobulin (Ig) gene segments determines an individual's naive Ig repertoire and, consequently, (auto)antigen recognition. VDJ recombination follows probabilistic rules that can be modeled statistically. So far, it remains unknown whether VDJ recombination rules differ between individuals. If these rules differed, identical (auto)antigen-specific Ig sequences would be generated with individual-specific probabilities, signifying that the available Ig sequence space is individual specific. We devised a sensitivity-tested distance measure that enables inter-individual comparison of VDJ recombination models. We discovered, accounting for several sources of noise as well as allelic variation in Ig sequencing data, that not only unrelated individuals but also human monozygotic twins and even inbred mice possess statistically distinguishable immunoglobulin recombination models. This suggests that, in addition to genetic, there is also nongenetic modulation of VDJ recombination. We demonstrate that population-wide individualized VDJ recombination can result in orders of magnitude of difference in the probability to generate (auto)antigen-specific Ig sequences. Our findings have implications for immune receptor–based individualized medicine approaches relevant to vaccination, infection, and autoimmunity.
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Akbar, Rahmad; Robert, Philippe Paul Auguste; Pavlović, Milena; Jeliazkov, Jeliazko R.; Snapkov, Igor & Slabodkin, Andrei
[Show all 15 contributors for this article]
(2021).
A compact vocabulary of paratope-epitope interactions enables predictability of antibody-antigen binding.
Cell reports.
34:108856(11),
p. 1–21.
doi:
10.1016/j.celrep.2021.108856.
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Antibody-antigen binding relies on the specific interaction of amino acids at the paratope-epitope interface. The predictability of antibody-antigen binding is a prerequisite for de novo antibody and (neo-)epitope design. A fundamental premise for the predictability of antibody-antigen binding is the existence of paratope- epitope interaction motifs that are universally shared among antibody-antigen structures. In a dataset of non-redundant antibody-antigen structures, we identify structural interaction motifs, which together compose a commonly shared structure-based vocabulary of paratope-epitope interactions. We show that this vocabulary enables the machine learnability of antibody-antigen binding on the paratope-epitope level using generative machine learning. The vocabulary (1) is compact, less than 104 motifs; (2) distinct from non-immune protein-protein interactions; and (3) mediates specific oligo- and polyreactive interactions between paratope-epitope pairs. Our work leverages combined structure- and sequence-based learning to demonstrate that machine-learning-driven predictive paratope and epitope engineering is feasible.
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Wang, Yinzhi; Haff, Ingrid Hobæk & Huseby, Arne
(2020).
Modelling extreme claims via composite models and threshold selection methods.
Insurance, Mathematics & Economics.
ISSN 0167-6687.
91,
p. 257–268.
doi:
10.1016/j.insmatheco.2020.02.009.
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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 empirical rule has the overall best performance in terms of the quality of the reserve estimate. The second best are either the square root rule or the exponentiality test. The latter works better when the right tail of the data is extreme. As the sample size becomes small, the best performance is obtained with simultaneous estimation. 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≤b, the probability that a claim is below the threshold, is more robust than the theoretical one.
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Ko, Vinnie; Hjort, Nils Lid & Haff, Ingrid Hobæk
(2019).
Focused information criteria for copulae.
Scandinavian Journal of Statistics.
ISSN 0303-6898.
46,
p. 1117–1140.
doi:
10.1111/sjos.12387.
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In this paper, we extend the focused information criterion (FIC) to copula models. Copulas are often used for applications where the joint tail behavior of the variables is of particular interest, and selecting a copula that captures this well is then essential. Traditional model selection methods such as the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) aim at finding the overall best‐fitting model, which is not necessarily the one best suited for the application at hand. The FIC, on the other hand, evaluates and ranks candidate models based on the precision of their point estimates of a context‐given focus parameter. This could be any quantity of particular interest, for example, the mean, a correlation, conditional probabilities, or measures of tail dependence. We derive FIC formulae for the maximum likelihood estimator, the two‐stage maximum likelihood estimator, and the so‐called pseudo‐maximum‐likelihood (PML) estimator combined with parametric margins. Furthermore, we confirm the validity of the AIC formula for the PML estimator combined with parametric margins. To study the numerical behavior of FIC, we have carried out a simulation study, and we have also analyzed a multivariate data set pertaining to abalones. The results from the study show that the FIC successfully ranks candidate models in terms of their performance, defined as how well they estimate the focus parameter. In terms of estimation precision, FIC clearly outperforms AIC, especially when the focus parameter relates to only a specific part of the model, such as the conditional upper‐tail probability.
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Bevacqua, Emanuele; Maraun, Douglas; Haff, Ingrid Hobæk; Widmann, Matrin & Vrac, Mathieu
(2017).
Multivariate statistical modelling of compound events via pair-copula constructions: Analysis of floods in Ravenna (Italy).
Hydrology and Earth System Sciences (HESS).
ISSN 1027-5606.
21(6),
p. 2701–2723.
doi:
10.5194/hess-21-2701-2017.
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Compound events (CEs) are multivariate extreme events in which the individual contributing variables may not be extreme themselves, but their joint – dependent – occurrence causes an extreme impact. Conventional univariate statistical analysis cannot give accurate information regarding the multivariate nature of these events. We develop a conceptual model, implemented via pair-copula constructions, which allows for the quantification of the risk associated with compound events in present-day and future climate, as well as the uncertainty estimates around such risk. The model includes predictors, which could represent for instance meteorological processes that provide insight into both the involved physical mechanisms and the temporal variability of compound events. Moreover, this model enables multivariate statistical downscaling of compound events. Downscaling is required to extend the compound events' risk assessment to the past or future climate, where climate models either do not simulate realistic values of the local variables driving the events or do not simulate them at all. Based on the developed model, we study compound floods, i.e. joint storm surge and high river runoff, in Ravenna (Italy). To explicitly quantify the risk, we define the impact of compound floods as a function of sea and river levels. We use meteorological predictors to extend the analysis to the past, and get a more robust risk analysis. We quantify the uncertainties of the risk analysis, observing that they are very large due to the shortness of the available data, though this may also be the case in other studies where they have not been estimated. Ignoring the dependence between sea and river levels would result in an underestimation of risk; in particular, the expected return period of the highest compound flood observed increases from about 20 to 32 years when switching from the dependent to the independent case.
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Haff, Ingrid Hobæk; Aas, Kjersti; Frigessi, Arnoldo & Graziani, Virginia Lacal
(2016).
Structure learning in Bayesian Networks using regular vines.
Computational Statistics & Data Analysis.
ISSN 0167-9473.
101,
p. 186–208.
doi:
10.1016/j.csda.2016.03.003.
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Learning the structure of a Bayesian Network from multidimensional data is an important task in many situations, as it allows understanding conditional
(in)dependence relations which in turn can be used for prediction. Current methods mostly assume a multivariate normal or a discrete multinomial model. A new greedy learning algorithm for continuous non-Gaussian variables, where marginal distributions can be arbitrary, as well as the dependency structure, is proposed. It exploits the regular vine approximation of the model, which is a tree-based hierarchical construction with pair-copulae as building blocks. It is shown that the networks obtainable with our algorithm belong to a certain subclass of chordal graphs. Chordal graphs representations are often preferred,
as they allow very efficient message passing and information propagation in intervention studies. It is illustrated through several examples and real data applications that the possibility of using non-Gaussian margins and a nonnon-linear
dependency structure outweighs the restriction to chordal graphs.
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Haff, Ingrid Hobæk; Frigessi, Arnoldo & Maraun, Douglas
(2015).
How well do regional climate models simulate the spatial dependence of precipitation? An application of pair-copula constructions.
Journal of Geophysical Research (JGR): Atmospheres.
ISSN 2169-897X.
120(7),
p. 2624–2646.
doi:
10.1002/2014JD022748.
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We investigate how well a suite of regional climate models (RCMs) from the ENSEMBLES project represents the residual spatial dependence of daily precipitation. The study area we consider is a 200 km × 200 km region in south central Norway, with RCMs driven by ERA-40 boundary conditions at a horizontal resolution of approximately 25 km × 25 km. We model the residual spatial dependence with pair-copula constructions, which allows us to assess both the overall and tail dependence in precipitation, including uncertainty estimates. The selected RCMs reproduce the overall dependence rather well, though the discrepancies compared to observations are substantial. All models overestimate the overall dependence in the west-east direction. They also overestimate the upper tail dependence in the north-south direction during winter, and in the west-east direction during summer, whereas they tend to underestimate this dependence in the north-south direction in summer. Moreover, many of the climate models do not simulate the small-scale dependence patterns caused by the pronounced orography well. However, the misrepresented residual spatial dependence does not seem to affect estimates of high quantiles of extreme precipitation aggregated over a few grid boxes. The underestimation of the area-aggregated extreme precipitation is due mainly to the well-known underestimation of the univariate margins for individual grid boxes, suggesting that the correction of RCM biases in precipitation might be feasible.
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Haff, Ingrid Hobæk & Segers, Johan
(2014).
Nonparametric estimation of pair-copula constructions with the empirical pair-copula.
Computational Statistics & Data Analysis.
ISSN 0167-9473.
84,
p. 1–13.
doi:
10.1016/j.csda.2014.10.020.
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A pair-copula construction is a decomposition of a multivariate copula into a structured system, called regular vine, of bivariate copulae or pair-copulae. The standard practice is to model these pair-copulae parametrically, inducing a model risk, with errors potentially propagating throughout the vine structure. The empirical pair-copula provides a nonparametric alternative, which is conjectured to still achieve the parametric convergence rate. Its main advantage for the user is that it does not require the choice of parametric models for each of the pair-copulae constituting the construction. It can be used as a basis for inference on dependence measures, for selecting an appropriate vine structure, and for testing for conditional independence.
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Haff, Ingrid Hobæk
(2013).
Parameter estimation for pair-copula constructions.
Bernoulli.
ISSN 1350-7265.
19(2),
p. 462–491.
doi:
10.3150/12-BEJ413.
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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.
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Haff, Ingrid Hobæk
(2012).
Comparison of estimators for pair-copula constructions.
Journal of Multivariate Analysis.
ISSN 0047-259X.
110,
p. 91–105.
doi:
10.1016/j.jmva.2011.08.013.
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We compare two of the most used estimators for the parameters of a pair-copula construction (PCC), namely the semiparametric (SP) and the stepwise semiparametric (SSP) estimators. By construction, the computational speed of the SSP estimator is considerably higher, at the expense of its asymptotic efficiency. Based on an extensive simulation study, we find that the performance of the SSP estimator is overall satisfactory compared to its contender. SSP loses some efficiency with respect to SP with increasing dependence, especially in the top levels of the PCC. On the other hand, the SSP estimator may suffer less under reduced sample sizes and misspecification of the model. Finally, it is the only real alternative for large-dimensional problems. Though it struggles with the top level parameters, the lower order dependences of the resulting estimated PCC mimic the true distribution well. All in all, this study supports the use of SSP in most applications.
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Haff, Ingrid Hobæk; Griesbauer, Elisabeth Maria; Czado, Claudia & Frigessi, Arnoldo
(2026).
Synthetic data with vine copulas – balancing utility and privacy.
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Griesbauer, Elisabeth Maria; Czado, Claudia; Frigessi, Arnoldo & Haff, Ingrid Hobæk
(2025).
Synthetic data generation balancing privacy and utility, using vine copulas.
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The availability of high-quality data has led to tremendous advances in science, technology and society at large, when analysed by means of statistical and machine learning (ML) methods. However, real-world data in many cases cannot be made public to the research community due to privacy restrictions. This impairs progress especially in bio-medical research. Synthetic data can substitute the sensitive real data, as long as they do not disclose private aspects. This has proven to be successful in training downstream ML applications. We propose TVineSynth, a vine copula based synthetic tabular data generator. TVineSynth 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 differential privacy (DP) by globally adding noise, TVineSynth performs a controlled approximation of the estimated data generating distribution. Because of this 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. Combined with the specific tree structure of the vine, this causes the model to zero out privacy-leaking dependencies while relying on those that are beneficial for utility. We theoretically justify how the construction of TVineSynth ensures privacy. When compared to competitor models, with and without DP, TVineSynth achieves a superior privacy-utility balance.
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Griesbauer, Elisabeth Maria; Czado, Claudia; Frigessi, Arnoldo & Haff, Ingrid Hobæk
(2025).
Poster: TVineSynth: A Truncated C-Vine Copula Generator of Synthetic Tabular Data to Balance Privacy and Utility.
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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.
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Griesbauer, Elisabeth Maria; Czado, Claudia; Frigessi, Arnoldo & Haff, Ingrid Hobæk
(2025).
Poster: TVineSynth: A Truncated C-Vine Copula Generator of Synthetic Tabular Data to Balance Privacy and Utility.
Full text in Research Archive
Show summary
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.
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Griesbauer, Elisabeth Maria; Czado, Claudia; Frigessi, Arnoldo & Haff, Ingrid Hobæk
(2024).
Synthetic data generation balancing privacy and utility, using vine copulas.
doi:
https:/nva.sikt.no/registration/0199812d9067-f1497889-e36d-4995-8686-7c68d1e99cdb/edit.
Full text in Research Archive
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The availability of diverse, high-quality data has led to tremendous advances in science, technology and society at large, when analysed by means of statistical and machine learning
(ML) methods. However, real-world data, in many cases, cannot be made public to the research community due to privacy restrictions, obstructing progress, especially in bio-
medical research. Synthetic data can substitute the sensitive real data, and as long as they do not disclose private aspects. This has proven to be successful in training downstream ML applications. 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 differential privacy (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 compa red to competitor models, with and without DP, on simulated and on real-world data, TVineSynth achieves a superior privacy-utility balance.
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Haff, Ingrid Hobæk; Griesbauer, Elisabeth Maria; Frigessi, Arnoldo & Czado, Claudia
(2024).
Synthetic data with vine copulas – balancing utility and privacy.
Full text in Research Archive
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Haff, Ingrid Hobæk; Brant, Simon Boge & Bakka, Haakon Christopher
(2024).
An explainable vine copula- based generalisation of logistic regression.
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Haff, Ingrid Hobæk; Brant, Simon Boge & Bakka, Haakon Christopher
(2024).
Generalised logistic regression with vine copulas.
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Haff, Ingrid Hobæk; Griesbauer, Elisabeth Maria; Frigessi, Arnoldo & Czado, Claudia
(2024).
Synthetic data with vine copulas – balancing utility and privacy.
Full text in Research Archive
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Haff, Ingrid Hobæk; Brant, Simon Boge & Bakka, Haakon Christopher
(2023).
A copula-based extension of logistic regression.
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Haff, Ingrid Hobæk; Griesbauer, Elisabeth Maria; Frigessi, Arnoldo & Czado, Claudia
(2023).
Synthetic data with vine-copulas - balancing utility and privacy.
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Haff, Ingrid Hobæk
(2022).
Masterprogramene i statistikk og data science ved Universitetet i Oslo – likheter og forskjeller.
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Sandve, Geir Kjetil Ferkingstad; Greiff, Victor; Haff, Ingrid Hobæk & Vu, Mai Ha
(2022).
Deciphering the Immune System Through Linguistics-Inspired Statistical Machine Learning.
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Wang, Yinzhi & Haff, Ingrid Hobæk
(2018).
Modelling extreme claims via composite models and threshold selection methods.
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Haff, Ingrid Hobæk & Segers, Johan
(2018).
Nonparametric estimation of pair-copula constructions with the empirical pair-copula.
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Haff, Ingrid Hobæk & Wang, Yinzhi
(2018).
Focussed selection of the claim severity distribution in non-life insurance.
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Løland, Anders; Berset, Anders & Haff, Ingrid Hobæk
(2017).
Er maskinlæring framtida i Skatteetaten?
Praktisk Økonomi & Finans.
ISSN 1501-0074.
33(3),
p. 344–352.
doi:
10.18261/issn.1504-2871-2017-03-06.
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Skatteetaten bruker i dag prediktive metoder til blant annet utvelgelse til kontroll av merverdiavgiftsoppgaver og til å forbedre og effektivisere innkreving av skatter. Dette har vist seg å gi økt proveny og en mer effektiv utnyttelse av ressursene. Framover ønsker Skatteetaten å få utviklet nye modeller som vil forenkle rapporteringen for den delen av næringslivet som opererer innenfor lovverket, og samtidig gjør kampen mot svart økonomi mer effektiv. Derfor har etaten inngått partnerskap med Big Insight, som er et såkalt Senter for forskningsdrevet innovasjon. Big Insight består av forskningspartnere, private bedrifter og offentlige etater, og skal forske på innovative statistikk- og maskinlæringsmetoder for å løse viktige problemer. Hovedformålet med samarbeidet mellom Skatteetaten og Big Insight er å utvikle metodikk som gjør det mulig å ta i bruk stadig nye datakilder og økte datamengder for å målrette veiledning, kommunikasjon, forebygging og forenkling av kontrollarbeidet.
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Haff, Ingrid Hobæk & Segers, Johan
(2016).
Nonparametric estimation of pair-copula constructions with the empirical pair-copula.
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Haff, Ingrid Hobæk
(2016).
How well do regional climate models simulate the spatial dependence of precipitation? An application of pair-copula constructions.
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Haff, Ingrid Hobæk; Frigessi, Arnoldo & Maraun, Douglas
(2015).
Hvor godt klarer regionale klimamodeller å gjenskape den romlige avhengigheten i nedbør?
Full text in Research Archive
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Haff, Ingrid Hobæk; Frigessi, Arnoldo & Maraun, Douglas
(2015).
How well do regional climate models simulate the
spatial dependence of precipitation? An
application of pair-copula constructions.
Full text in Research Archive
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Løland, Anders; Lenkoski, Alex; Haff, Ingrid Hobæk & Neef, Linda Reiersølmoen
(2014).
Calibrated Probabilities and the Investigation of Soft Fraud in Automobile Insurance Claims.
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Aas, Kjersti; Haff, Ingrid Hobæk & Dimakos, Xeni Kristine
(2007).
Risk Estimation using the Multivariate Normal Inverse Gaussian Distribution.
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View all works in NVA
Published
Oct. 1, 2015 11:42 AM
- Last modified
Dec. 14, 2022 10:04 AM
