CLAX is a JAX-based library that implements classic click models using modern gradient-based optimization. While neural click models have emerged over the past decade, complex click models based on probabilistic graphical models (PGMs) have not systematically adopted gradient-based optimization, preventing practitioners from leveraging modern deep learning frameworks while preserving the interpretability of classic models. CLAX addresses this gap by replacing EM-based optimization with direct gradient-based optimization in a numerically stable manner. The framework's modular design enables the integration of any component, from embeddings and deep networks to custom modules, into classic click models for end-to-end optimization. We demonstrate CLAX's efficiency by running experiments on the full Baidu-ULTR dataset comprising over a billion user sessions in $\approx$ 2 hours on a single GPU, orders of magnitude faster than traditional EM approaches. CLAX implements ten classic click models, serving both industry practitioners seeking to understand user behavior and improve ranking performance at scale and researchers developing new click models. CLAX is available at: https://github.com/philipphager/clax

Performative predictions are forecasts which influence the outcomes they aim to predict, undermining the existence of correct forecasts and standard methods of elicitation and estimation. We show that conditioning forecasts on covariates that separate them from the outcome renders the target distribution forecast-invariant, guaranteeing well-posedness of the forecasting problem. However, even under this condition, classical proper scoring rules fail to elicit correct forecasts. We prove a general impossibility result and identify two solutions: (i) in decision-theoretic settings, elicitation of correct and incentive-compatible forecasts is possible if forecasts are separating; (ii) scoring with unbiased estimates of the divergence between the forecast and the induced distribution of the target variable yields correct forecasts. Applying these insights to parameter estimation, conditional forecasts and proper scoring rules enable performatively stable estimation of performatively correct parameters, resolving the issues raised by Perdomo et al. (2020). Our results expose fundamental limits of classical forecast evaluation and offer new tools for reliable and accurate forecasting in performative settings.

Reasoning about fairness through correlation-based notions is rife with pitfalls. The 1973 University of California, Berkeley graduate school admissions case from \citet{BickelHO75} is a classic example of one such pitfall, namely Simpson’s paradox. The discrepancy in admission rates among male and female applicants, in the aggregate data over all departments, vanishes when admission rates per department are examined. We reason about the Berkeley graduate school admissions case through a causal lens. In the process, we introduce a statistical test for causal hypothesis testing based on Pearl’s instrumental-variable inequalities \citep{Pearl95}. We compare different causal notions of fairness that are based on graphical, counterfactual and interventional queries on the causal model, and develop statistical tests for these notions that use only observational data. We study the logical relations between notions, and show that while notions may not be equivalent, their corresponding statistical tests coincide for the case at hand. We believe that a thorough case-based causal analysis helps develop a more principled understanding of both causal hypothesis testing and fairness.

Unbiased learning-to-rank (ULTR) is a well-established framework for learning from user clicks, which are often biased by the ranker collecting the data. While theoretically justified and extensively tested in simulation, ULTR techniques lack empirical validation, especially on modern search engines. The Baidu-ULTR dataset released for the WSDM Cup 2023, collected from Baidu's search engine, offers a rare opportunity to assess the real-world performance of prominent ULTR techniques. Despite multiple submissions during the WSDM Cup 2023 and the subsequent NTCIR ULTRE-2 task, it remains unclear whether the observed improvements stem from applying ULTR or other learning techniques.

When estimating a regression model, we might have data where some labels are missing, or our data might be biased by a selection mechanism. When the response or selection mechanism is ignorable (i.e., independent of the response variable given the features) one can use off-the-shelf regression methods; in the nonignorable case one typically has to adjust for bias. We observe that privileged information (i.e. information that is only available during training) might render a nonignorable selection mechanism ignorable, and we refer to this scenario as Privilegedly Missing at Random (PMAR). We propose a novel imputation-based regression method, named repeated regression, that is suitable for PMAR. We also consider an importance weighted regression method, and a doubly robust combination of the two. The proposed methods are easy to implement with most popular out-of-the-box regression algorithms. We empirically assess the performance of the proposed methods with extensive simulated experiments and on a synthetically augmented real-world dataset. We conclude that repeated regression can appropriately correct for bias, and can have considerable advantage over weighted regression, especially when extrapolating to regions of the feature space where response is never observed.

Recommender systems have received much attention in recent years, and they have been successfully applied in many different domains. With each domain come new constraints that require system designers to make choices about how to apply and extend generic algorithms in their context. Booking.com is planet earth's number one accommodation reservation site. The accommodation recommendation problem that it needs to solve has several interesting and unique challenges that make that a straightforward matrix factorization or a basic bi-linear model are not sufficient to provide the required predictions. In this talk, we will discuss several of the challenges we have encountered and solutions we have developed.

On-street parking, just as any publicly owned utility, is used inefficiently if access is free or priced very far from market rates. This paper introduces a novel demand management solution: using data from dedicated occupancy sensors an iteration scheme updates parking rates to better match demand. The new rates encourage parkers to avoid peak hours and peak locations and reduce congestion and underuse. The solution is deliberately simple so that it is easy to understand, easily seen to be fair and leads to parking policies that are easy to remember and act upon. We study the convergence properties of the iteration scheme and prove that it converges to a reasonable distribution for a very large class of models. The algorithm is in use to change parking rates in over 6000 spaces in downtown Los Angeles since June 2012 as part of the LA Express Park project. Initial results are encouraging with a reduction of congestion and underuse, while in more locations rates were decreased than increased.

We propose a new sparse Bayesian model for multi-task regression and classification. The model is able to capture correlations between tasks, or more specifically a low-rank approximation of the covariance matrix, while being sparse in the features. We introduce a general family of group sparsity inducing priors based on matrix-variate Gaussian scale mixtures. We show the amount of sparsity can be learnt from the data by combining an approximate inference approach with type II maximum likelihood estimation of the hyperparameters. Empirical evaluations on data sets from biology and vision demonstrate the applicability of the model, where on both regression and classification tasks it achieves competitive predictive performance compared to previously proposed methods.

We propose a deterministic method to evaluate the integral of a positive function based on soft-binning functions that smoothly cut the integral into smaller integrals that are easier to approximate. In combination with mean-field approximations for each individual sub-part this leads to a tractable algorithm that alternates between the optimization of the bins and the approximation of the local integrals. We introduce suitable choices for the binning functions such that a standard mean field approximation can be extended to a split mean field approximation without the need for extra derivations. The method can be seen as a revival of the ideas underlying the mixture mean field approach. The latter can be obtained as a special case by taking soft-max functions for the binning.

Search engine click logs provide an invaluable source of relevance information, but this information is biased. A key source of bias is presentation order: the probability of click is influenced by a document's position in the results page. This paper focuses on explaining that bias, modelling how probability of click depends on position. We propose four simple hypotheses about how position bias might arise. We carry out a large data-gathering effort, where we perturb the ranking of a major search engine, to see how clicks are affected. We then explore which of the four hypotheses best explains the real-world position effects, and compare these to a simple logistic regression model. The data are not well explained by simple position models, where some users click indiscriminately on rank 1 or there is a simple decay of attention over ranks. A 'cascade' model, where users view results from top to bottom and leave as soon as they see a worthwhile document, is our best explanation for position bias in early ranks

We study the problem of learning two regimes (we have a normal and a prefault regime in mind) based on a train set of non-Markovian observation sequences. Key to the model is that we assume that once the system switches from the normal to the prefault regime it cannot restore and will eventually result in a fault. We refer to the particular setting as semi-supervised since we assume the only information given to the learner is whether a particular sequence ended with a stop (implying that the sequence was generated by the normal regime) or with a fault (implying that there was a switch from the normal to the fault regime). In the latter case the particular time point at which a switch occurred is not known. The underlying model used is a switching linear dynamical system (SLDS). The constraints in the regime transition probabilities result in an exact inference procedure that scales quadratically with the length of a sequence. Maximum aposteriori (MAP) parameter estimates can be found using an expectation maximization (EM) algorithm with this inference algorithm in the E-step. For long sequences this will not be practically feasible and an approximate inference and an approximate EM procedure is called for. We describe a flexible class of approximations corresponding to different choices of clusters in a Kikuchi free energy with weak consistency constraints.

We discuss the integration of the expectation-maximization (EM) algorithm for maximum likelihood learning of Bayesian networks with belief propagation algorithms for approximate inference. Specifically we propose to combine the outer-loop step of convergent belief propagation algorithms with the M-step of the EM algorithm. This then yields an approximate EM algorithm that is essentially still double loop, with the important advantage of an inner loop that is guaranteed to converge. Simulations illustrate the merits of such an approach.

We propose a novel visualization algorithm for high-dimensional time-series data. In contrast to most visualization techniques, we do not assume consecutive data points to be independent. The basic model is a linear dynamical system which can be seen as a dynamic extension of a probabilistic principal component model. A further extension to a particular switching linear dynamical system allows a representation of complex data onto multiple and even a hierarchy of plots. Using sensible approximations based on expectation propagation, the projections can be performed in essentially the same order of complexity as their static counterpart. We apply our method on a real-world data set with sensor readings from a paper machine.