#01Nov 12, 2026
stat.ML
Quantifying structural stability of transparent models for general insurance pricing
Félix Côté, Marie-Pier Côté
The short duration of general insurance contracts leads to rapid distributional shifts in the data, warranting regular model updates. This process may yield a post-update model that differs considerably from the pre-update model in both predictions and structure. Structural stability is upstream of predictive stability, yet existing structural stability metrics are mostly restricted to simple decision trees. Thus, we first introduce the notion of functional transparency, characterising models with a prediction function that can be expressed as a sum of univariate functions for main effects and bivariate functions for pairwise interactions. Then, we propose the Mean Squared Shape function distance, a metric to quantify the structural stability of functionally transparent models, which are particularly relevant in actuarial science. Using three public auto insurance datasets, we present a benchmark study to demonstrate the usefulness of our metric in identifying a stable and accurate transparent model. Generalised linear models with centred numerical covariates are stable, and explainable boosting machines (EBMs) offer a compromise between stability and performance. We also find that stabilisation strategies, such as sequential modelling and fixed hyperparameters, can substantially improve stability for both EBM and XGBoost models, with negligible impact on performance.
#02Nov 12, 2026
math.ST
Linear Regression with Self-Selection Bias in Polynomial Time
Felix Zhou
We revisit the problem of estimating $k$ linear regressors with self-selection bias in $n$ dimensions up to error $\varepsilon$ with the maximum self-selection criterion, as introduced by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [CDIZ23, STOC]. Our main result is a $\mathrm{poly}(n,k,1/\varepsilon)$ time algorithm for the unknown-index variant of this problem, thereby improving upon the running times of the best known algorithms due to Gaitonde and Mossel [GM24] and Kalavasis, Mehrotra, and Zhou [KMZ26, COLT] with exponential dependence on $k$. Our algorithm succeeds in the presence of correlated noise between regressors, which captures the related setting of max-affine regression. Consequently, we also give the first polynomial-time algorithm for this problem, improving on the prior works of Ghosh, Pananjady, Guntuboyina, and Ramchandran [GPGR22, IEEE Transactions on Information Theory] and Gaitonde and Mossel [GM24] with exponential dependence on $k$. Prior works exhaustively search over a $k$-dimensional subspace spanned by the regressors, using conditional moments of the response to test candidates. In contrast, our algorithm is driven by an improved understanding of the moments of the covariates. We show that, restricting to observations with large response values, the degree-$(\log n)$ Hermite moment of the covariates approximately decomposes as a sum of tensor powers of the regressors. The first step of our algorithm can be viewed as a tensor decomposition algorithm for these implicitly represented high-order tensors, which outputs unit vectors parallel to the regressors. A secondary step based on a simple variant of ordinary least squares extracts estimates for the regressors given these unit vectors. We believe our analytic insight and algorithmic components may have applications to designing efficient algorithms for other latent-variable problems.
#03Nov 12, 2026
cs.LG
A Convex-Analytic Reformulation for Poisoning Attacks on Logistic Regression
Carina Moreira Costa, Maria Eduarda Pinheiro, Martin Schmidt
We study data poisoning attacks on logistic regression with $\ell_2$-regularization, where an attacker chooses the features of a fixed number of injected observations with prescribed labels to maximize the logistic loss on the clean training data. Strong convexity of the defender's problem yields an exact reformulation through its first-order optimality conditions. Using convex conjugacy of the softplus function, we replace the sigmoid relations by a single convex optimality-gap inequality and express the attacker's objective as a concave function. A change of variables makes the stationarity condition affine, leaving bounded bilinear equalities as the only nonconvex constraints. We derive finite bounds on all variables involved in these equalities, including a global bound on the coefficient norm and tighter bounds obtained by preprocessing based on convex optimization. Experiments on eight binary classification datasets evaluate attack effectiveness and compare the two reformulations when solved with \textsf{SCIP}. Attacks obtained by local optimization degrade predictive performance on most datasets, while the convex-analytic formulation produces substantially stronger reported dual bounds within a fixed time limit.
#04Nov 12, 2026
cs.LG
Two mathematical models of knowledge distillation
Audrey Xie, Ludwig Schmidt, John Duchi
Many hypotheses compete to explain the successes of knowledge distillation. To help address this, we propose and analyze a mathematical model of distillation, which suggests that distillation's performance comes not from obtaining better models but from easier to optimize landscapes. For generalized linear models trained with stochastic gradient descent, we prove that distillation fits performant student models asymptotically more quickly than non-distilled models. In rank-1 matrix approximation, we characterize conditions on the target matrix under which gradient descent with distillation converges strictly faster than training on the supervised objective. The theory helps delineate the ways distillation provides benefits (i.e., in optimization speed, not in generalization), and experiments on real datasets corroborate the theoretical predictions.
#05Nov 12, 2026
eess.IV
Data Archive for 2D and 3D Electrical Impedance Tomography with moderate conductivity contrast phantoms
S. J. Hamilton, A. Hauptmann, A. Hänninen and 4 more
This document describes open Electrical Impedance Tomography (EIT) measurement data that were collected from biomedical imaging inspired phantoms with moderate conductivity contrasts. The data were collected with the KIT4 and KIT5 EIT measurement devices at the University of Eastern Finland, and are intended for EIT image reconstruction algorithm development and testing. The data from thoracic imaging inspired cylindrical and chest-shaped phantoms are suitable for 2D algorithms, and the data from an intracerebral hemorrhage imaging inspired head-shaped phantom with resistive skull are suitable for 3D algorithms. In addition to the measurement data, computational meshes and example reconstruction codes are provided and sample reconstructions included.