Causal Inference plays an significant role in explaining the decisions taken by statistical models and artificial intelligence models. Of late, this field started attracting the attention of researchers and practitioners alike. This paper presents a comprehensive survey of 37 papers published during 1992-2023 and concerning the application of causal inference to banking, finance, and insurance. The papers are categorized according to the following families of domains: (i) Banking, (ii) Finance and its subdomains such as corporate finance, governance finance including financial risk and financial policy, financial economics, and Behavioral finance, and (iii) Insurance. Further, the paper covers the primary ingredients of causal inference namely, statistical methods such as Bayesian Causal Network, Granger Causality and jargon used thereof such as counterfactuals. The review also recommends some important directions for future research. In conclusion, we observed that the application of causal inference in the banking and insurance sectors is still in its infancy, and thus more research is possible to turn it into a viable method.

Causal discovery aims at revealing causal relations from observational data, which is a fundamental task in science and engineering. We describe $\textit{causal-learn}$, an open-source Python library for causal discovery. This library focuses on bringing a comprehensive collection of causal discovery methods to both practitioners and researchers. It provides easy-to-use APIs for non-specialists, modular building blocks for developers, detailed documentation for learners, and comprehensive methods for all. Different from previous packages in R or Java, $\textit{causal-learn}$ is fully developed in Python, which could be more in tune with the recent preference shift in programming languages within related communities. The library is available at https://github.com/py-why/causal-learn.

Statistical prediction models are often trained on data from different probability distributions than their eventual use cases. One approach to proactively prepare for these shifts harnesses the intuition that causal mechanisms should remain invariant between environments. Here we focus on a challenging setting in which the causal and anticausal variables of the target are unobserved. Leaning on information theory, we develop feature selection and engineering techniques for the observed downstream variables that act as proxies. We identify proxies that help to build stable models and moreover utilize auxiliary training tasks to answer counterfactual questions that extract stability-enhancing information from proxies. We demonstrate the effectiveness of our techniques on synthetic and real data.

ML models are ubiquitous in real world applications and are a constant focus of research. At the same time, the community has started to realize the importance of protecting the privacy of ML training data. Differential Privacy (DP) has become a gold standard for making formal statements about data anonymization. However, while some adoption of DP has happened in industry, attempts to apply DP to real world complex ML models are still few and far between. The adoption of DP is hindered by limited practical guidance of what DP protection entails, what privacy guarantees to aim for, and the difficulty of achieving good privacy-utility-computation trade-offs for ML models. Tricks for tuning and maximizing performance are scattered among papers or stored in the heads of practitioners. Furthermore, the literature seems to present conflicting evidence on how and whether to apply architectural adjustments and which components are "safe" to use with DP. This work is a self-contained guide that gives an in-depth overview of the field of DP ML and presents information about achieving the best possible DP ML model with rigorous privacy guarantees. Our target audience is both researchers and practitioners. Researchers interested in DP for ML will benefit from a clear overview of current advances and areas for improvement. We include theory-focused sections that highlight important topics such as privacy accounting and its assumptions, and convergence. For a practitioner, we provide a background in DP theory and a clear step-by-step guide for choosing an appropriate privacy definition and approach, implementing DP training, potentially updating the model architecture, and tuning hyperparameters. For both researchers and practitioners, consistently and fully reporting privacy guarantees is critical, and so we propose a set of specific best practices for stating guarantees.

Reed-Muller (RM) codes achieve the capacity of general binary-input memoryless symmetric channels and are conjectured to have a comparable performance to that of random codes in terms of scaling laws. However, such results are established assuming maximum-likelihood decoders for general code parameters. Also, RM codes only admit limited sets of rates. Efficient decoders such as successive cancellation list (SCL) decoder and recently-introduced recursive projection-aggregation (RPA) decoders are available for RM codes at finite lengths. In this paper, we focus on subcodes of RM codes with flexible rates. We first extend the RPA decoding algorithm to RM subcodes. To lower the complexity of our decoding algorithm, referred to as subRPA, we investigate different approaches to prune the projections. Next, we derive the soft-decision based version of our algorithm, called soft-subRPA, that not only improves upon the performance of subRPA but also enables a differentiable decoding algorithm. Building upon the soft-subRPA algorithm, we then provide a framework for training a machine learning (ML) model to search for \textit{good} sets of projections that minimize the decoding error rate. Training our ML model enables achieving very close to the performance of full-projection decoding with a significantly smaller number of projections. We also show that the choice of the projections in decoding RM subcodes matters significantly, and our ML-aided projection pruning scheme is able to find a \textit{good} selection, i.e., with negligible performance degradation compared to the full-projection case, given a reasonable number of projections.

Application for semantic segmentation models in areas such as autonomous vehicles and human computer interaction require real-time predictive capabilities. The challenges of addressing real-time application is amplified by the need to operate on resource constrained hardware. Whilst development of real-time methods for these platforms has increased, these models are unable to sufficiently reason about uncertainty present when applied on embedded real-time systems. This paper addresses this by combining deep feature extraction from pre-trained models with Bayesian regression and moment propagation for uncertainty aware predictions. We demonstrate how the proposed method can yield meaningful epistemic uncertainty on embedded hardware in real-time whilst maintaining predictive performance.

The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems. In this article, we propose a data-driven framework combining Reservoir Computing and Normalizing Flow to study this issue, which mimics error modeling to improve traditional Reservoir Computing performance and integrates the virtues of both approaches. With few assumptions about the underlying stochastic dynamical systems, this model-free method successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors. We verify the effectiveness of the proposed framework in several experiments, including the stochastic Van der Pal oscillator, El Ni\~no-Southern Oscillation simplified model, and stochastic Lorenz system. These experiments consist of Markov/non-Markov and stationary/non-stationary stochastic processes which are defined by linear/nonlinear stochastic differential equations or stochastic delay differential equations. Additionally, we explore the noise-induced tipping phenomenon, relaxation oscillation, stochastic mixed-mode oscillation, and replication of the strange attractor.

The utilization of model checking has been suggested as a formal verification technique for analyzing critical systems. However, the primary challenge in applying to complex systems is state space explosion problem. To address this issue, bisimulation minimization has emerged as a prominent method for reducing the number of states in a labeled transition system, aiming to overcome the difficulties associated with the state space explosion problem. In the case of systems exhibiting stochastic behaviors, probabilistic bisimulation is employed to minimize a given model, obtaining its equivalent form with fewer states. Recently, various techniques have been introduced to decrease the time complexity of the iterative methods used to compute probabilistic bisimulation for stochastic systems that display nondeterministic behaviors. In this paper, we propose a new technique to partition the state space of a given probabilistic model to its bisimulation classes. This technique uses the PRISM program of a given model and constructs some small versions of the model to train a classifier. It then applies machine learning classification techniques to approximate the related partition. The resulting partition is used as an initial one for the standard bisimulation technique in order to reduce the running time of the method. The experimental results show that the approach can decrease significantly the running time compared to state-of-the-art tools.

We consider a general optimization problem of minimizing a composite objective functional defined over a class of probability distributions. The objective is composed of two functionals: one is assumed to possess the variational representation and the other is expressed in terms of the expectation operator of a possibly nonsmooth convex regularizer function. Such a regularized distributional optimization problem widely appears in machine learning and statistics, such as proximal Monte-Carlo sampling, Bayesian inference and generative modeling, for regularized estimation and generation. We propose a novel method, dubbed as Moreau-Yoshida Variational Transport (MYVT), for solving the regularized distributional optimization problem. First, as the name suggests, our method employs the Moreau-Yoshida envelope for a smooth approximation of the nonsmooth function in the objective. Second, we reformulate the approximate problem as a concave-convex saddle point problem by leveraging the variational representation, and then develope an efficient primal-dual algorithm to approximate the saddle point. Furthermore, we provide theoretical analyses and report experimental results to demonstrate the effectiveness of the proposed method.

The practical utility of causality in decision-making is widespread and brought about by the intertwining of causal discovery and causal inference. Nevertheless, a notable gap exists in the evaluation of causal discovery methods, where insufficient emphasis is placed on downstream inference. To address this gap, we evaluate seven established baseline causal discovery methods including a newly proposed method based on GFlowNets, on the downstream task of treatment effect estimation. Through the implementation of a distribution-level evaluation, we offer valuable and unique insights into the efficacy of these causal discovery methods for treatment effect estimation, considering both synthetic and real-world scenarios, as well as low-data scenarios. The results of our study demonstrate that some of the algorithms studied are able to effectively capture a wide range of useful and diverse ATE modes, while some tend to learn many low-probability modes which impacts the (unrelaxed) recall and precision.