Point processes are widely used statistical tools for modeling event occurrence patterns within continuous spatio-temporal domains.

The joint probabilities of potential outcomes are fundamental components of causal inference in the sense that (i) if they are identifiable, then the causal risk is also identifiable, but not vise versa (Pearl, 2009; Tian and Pearl, 2000) and (ii) they enable us to evaluate the probabilistic aspects of sufficiency'', and ``necessity and sufficiency'', which are important concepts of successful explanation (Watson, et al., 2020). However, because they are not identifiable without any assumptions, various assumptions have been utilized to evaluate the joint probabilities of potential outcomes, e.g., the assumption of monotonicity (Pearl, 2009; Tian and Pearl, 2000), the independence between potential outcomes (Robins and Richardson, 2011), the condition of gain equality (Li and Pearl, 2019), and the specific functional relationships between cause and effect (Pearl, 2009). Unlike existing identification conditions, in order to evaluate the joint probabilities of potential outcomes without such assumptions, this paper proposes two types of novel identification conditions using covariate information. In addition, when the joint probabilities of potential outcomes are identifiable through the proposed conditions, the estimation problem of the joint probabilities of potential outcomes reduces to that of singular models and thus they can not be evaluated by standard statistical estimation methods. To solve the problem, this paper proposes a new statistical estimation method based on the augmented Lagrangian method and shows the asymptotic normality of the proposed estimators. Given space constraints, the proofs, the details on the statistical estimation method, some numerical experiments, and the case study are provided in the supplementary material.

Point processes are widely used statistical tools for modeling event occurrence patterns within continuous spatio-temporal domains.

In most real world decision problems, the decision maker (DM) faces uncertainty either in the objective function that he aims to optimize, or some of the constraints that he needs to satisfy.

The joint probabilities of potential outcomes are fundamental components of causal inference in the sense that (i) if they are identifiable, then the causal risk is also identifiable, but not vise versa (Pearl, 2009; Tian and Pearl, 2000) and (ii) they enable us to evaluate the probabilistic aspects of necessity'',sufficiency'', and necessity and sufficiency'', which are important concepts of successful explanation (Watson, et al., 2020). However, because they are not identifiable without any assumptions, various assumptions have been utilized to evaluate the joint probabilities of potential outcomes, e.g., the assumption of monotonicity (Pearl, 2009; Tian and Pearl, 2000), the independence between potential outcomes (Robins and Richardson, 2011), the condition of gain equality (Li and Pearl, 2019), and the specific functional relationships between cause and effect (Pearl, 2009). Unlike existing identification conditions, in order to evaluate the joint probabilities of potential outcomes without such assumptions, this paper proposes two types of novel identification conditions using covariate information. In addition, when the joint probabilities of potential outcomes are identifiable through the proposed conditions, the estimation problem of the joint probabilities of potential outcomes reduces to that of singular models and thus they can not be evaluated by standard statistical estimation methods. To solve the problem, this paper proposes a new statistical estimation method based on the augmented Lagrangian method and shows the asymptotic normality of the proposed estimators. Given space constraints, the proofs, the details on the statistical estimation method, some numerical experiments, and the case study are provided in the supplementary material.

Feed-forward neural networks (FNNs) provide state-of-the-art deep learning regression models for actuarial pricing. FNNs can be seen as extensions of generalized linear models (GLMs), taking covariates as inputs to these FNNs, feature-engineering these covariates through several hidden FNN layers, and then using these feature-engineered covariates as inputs to a GLM. Advantages of FNNs over classical GLMs are that they are able to find functional forms and interactions in the covariates that cannot easily be captured by GLMs, and which typically require the modeler to have specific deeper insights into the data generation process. Since these specific deeper insights are not always readily available, FNNs may support the modeler in finding such structure and insight. Taking inspiration from the recent huge success of large language models (LLMs), the natural question arises whether there are network architectures other than FNNs that share more similarity with LLMs and which can further improve predictive performance of neural networks in actuarial pricing. LLMs are based on the Transformer architecture which has been invented by Vaswani et al. [31]. The Transformer architecture is based on attention layers which are special network modules that allow covariate components to communicate with each other.

In traditional Machine Learning, the algorithms predictions are based on the assumption that the data follows the same distribution in both the training and the test datasets. However, in real world data this condition does not hold and, for instance, the distribution of the covariates changes whereas the conditional distribution of the targets remains unchanged. This situation is called covariate shift problem where standard error estimation may be no longer accurate. In this context, the importance is a measure commonly used to alleviate the influence of covariate shift on error estimations. The main drawback is that it is not easy to compute. The Kullback-Leibler Importance Estimation Procedure (KLIEP) is capable of estimating importance in a promising way. Despite its good performance, it fails to ignore target information, since it only includes the covariates information for computing the importance. In this direction, this paper explores the potential performance improvement if target information is considered in the computation of the importance. Then, a redefinition of the importance arises in order to be generalized in this way. Besides the potential improvement in performance, including target information make possible the application to a real application about plankton classification that motivates this research and characterized by its great dimensionality, since considering targets rather than covariates reduces the computation and the noise in the covariates. The impact of taking target information is also explored when Logistic Regression (LR), Kernel Mean Matching (KMM), Ensemble Kernel Mean Matching (EKMM) and the naive predecessor of KLIEP called Kernel Density Estimation (KDE) methods estimate the importance. The experimental results lead to a more accurate error estimation using target information, especially in case of the more promising method KLIEP.

Learning from Label Proportions (LLP) is a learning problem where only aggregate level labels are available for groups of instances, called bags, during training, and the aim is to get the best performance at the instance-level on the test data. This setting arises in domains like advertising and medicine due to privacy considerations. We propose a novel algorithmic framework for this problem that iteratively performs two main steps. For the first step (Pseudo Labeling) in every iteration, we define a Gibbs distribution over binary instance labels that incorporates a) covariate information through the constraint that instances with similar covariates should have similar labels and b) the bag level aggregated label. We then use Belief Propagation (BP) to marginalize the Gibbs distribution to obtain pseudo labels. In the second step (Embedding Refinement), we use the pseudo labels to provide supervision for a learner that yields a better embedding. In the final iteration, a classifier is trained using the pseudo labels. Our algorithm displays strong gains against several SOTA baselines (up to 15%) for the LLP Binary Classification problem on various dataset types - tabular and Image. We achieve these improvements with minimal computational overhead above standard supervised learning due to Belief Propagation, for large bag sizes, even for a million samples. Learning from Label Proportions (henceforth LLP) has seen renewed interest in recent times due to the rising concerns of privacy and leakage of sensitive information (Ardehaly & Culotta, 2017; Busa-Fekete et al., 2023; Zhang et al., 2022; Kobayashi et al., 2022; Yu et al., 2014). In the LLP binary classification setting, all the training instances are aggregated into bags and only the aggregated label count for a bag is available, i.e. proportion of 1's in a bag. Features of all instances are available. This can be seen as a form of weak supervision compared to providing instance-level labels.

Focusing on stochastic programming (SP) with covariate information, this paper proposes an empirical risk minimization (ERM) method embedded within a nonconvex piecewise affine decision rule (PADR), which aims to learn the direct mapping from features to optimal decisions. We establish the nonasymptotic consistency result of our PADR-based ERM model for unconstrained problems and asymptotic consistency result for constrained ones. To solve the nonconvex and nondifferentiable ERM problem, we develop an enhanced stochastic majorization-minimization algorithm and establish the asymptotic convergence to (composite strong) directional stationarity along with complexity analysis. We show that the proposed PADR-based ERM method applies to a broad class of nonconvex SP problems with theoretical consistency guarantees and computational tractability. Our numerical study demonstrates the superior performance of PADR-based ERM methods compared to state-of-the-art approaches under various settings, with significantly lower costs, less computation time, and robustness to feature dimensions and nonlinearity of the underlying dependency.

The variational autoencoder (VAE) is a popular deep latent variable model used to analyse high-dimensional datasets by learning a low-dimensional latent representation of the data. It simultaneously learns a generative model and an inference network to perform approximate posterior inference. Recently proposed extensions to VAEs that can handle temporal and longitudinal data have applications in healthcare, behavioural modelling, and predictive maintenance. However, these extensions do not account for heterogeneous data (i.e., data comprising of continuous and discrete attributes), which is common in many real-life applications. In this work, we propose the heterogeneous longitudinal VAE (HL-VAE) that extends the existing temporal and longitudinal VAEs to heterogeneous data. HL-VAE provides efficient inference for high-dimensional datasets and includes likelihood models for continuous, count, categorical, and ordinal data while accounting for missing observations. We demonstrate our model's efficacy through simulated as well as clinical datasets, and show that our proposed model achieves competitive performance in missing value imputation and predictive accuracy.