The economic and banking importance of the small and medium enterprise (SME) sector is well recognized in contemporary society. Business credit loans are very important for the operation of SMEs, and the revenue is a key indicator of credit limit management. Therefore, it is very beneficial to construct a reliable revenue forecasting model. If the uncertainty of an enterprise's revenue forecasting can be estimated, a more proper credit limit can be granted. Natural gradient boosting approach, which estimates the uncertainty of prediction by a multi-parameter boosting algorithm based on the natural gradient. However, its original implementation is not easy to scale into big data scenarios, and computationally expensive compared to state-of-the-art tree-based models (such as XGBoost). In this paper, we propose a Scalable Natural Gradient Boosting Machines that is simple to implement, readily parallelizable, interpretable and yields high-quality predictive uncertainty estimates. According to the characteristics of revenue distribution, we derive an uncertainty quantification function. We demonstrate that our method can distinguish between samples that are accurate and inaccurate on revenue forecasting of SMEs. What's more, interpretability can be naturally obtained from the model, satisfying the financial needs.

Bayes' rule: (or Bayes' theorem) of one probability theory's most important rules, describing the probability of an event, based on prior knowledge of conditions that might be related:

In this paper, we target at recovering the exact routes taken by commuters inside a metro system that arenot captured by an Automated Fare Collection (AFC) system and hence remain unknown. We strategicallypropose two inference tasks to handle the recovering, one to infer the travel time of each travel link thatcontributes to the total duration of any trip inside a metro network and the other to infer the route preferencesbased on historical trip records and the travel time of each travel link inferred in the previous inferencetask. As these two inference tasks have interrelationship, most of existing works perform these two taskssimultaneously. However, our solutionTripDecoderadopts a totally different approach. To the best of ourknowledge,TripDecoderis the first model that points out and fully utilizes the fact that there are some tripsinside a metro system with only one practical route available. It strategically decouples these two inferencetasks by only taking those trip records with only one practical route as the input for the first inference taskof travel time and feeding the inferred travel time to the second inference task as an additional input whichnot only improves the accuracy but also effectively reduces the complexity of both inference tasks. Twocase studies have been performed based on the city-scale real trip records captured by the AFC systems inSingapore and Taipei to compare the accuracy and efficiency ofTripDecoderand its competitors. As expected,TripDecoderhas achieved the best accuracy in both datasets, and it also demonstrates its superior efficiencyand scalability.

Neural networks are known to suffer from catastrophic forgetting when trained on sequential datasets. While there have been numerous attempts to solve this problem for large-scale supervised classification, little has been done to overcome catastrophic forgetting for few-shot classification problems. We demonstrate that the popular gradient-based few-shot meta-learning algorithm Model-Agnostic Meta-Learning (MAML) indeed suffers from catastrophic forgetting and introduce a Bayesian online meta-learning framework that tackles this problem. Our framework incorporates MAML into a Bayesian online learning algorithm with Laplace approximation. This framework enables few-shot classification on a range of sequentially arriving datasets with a single meta-learned model. The experimental evaluations demonstrate that our framework can effectively prevent forgetting in various few-shot classification settings compared to applying MAML sequentially.

Modern causal inference methods allow machine learning to be used to weaken parametric modeling assumptions. However, the use of machine learning may result in bias and incorrect inferences due to overfitting. Cross-fit estimators have been proposed to eliminate this bias and yield better statistical properties. We conducted a simulation study to assess the performance of several different estimators for the average causal effect (ACE). The data generating mechanisms for the simulated treatment and outcome included log-transforms, polynomial terms, and discontinuities. We compared singly-robust estimators (g-computation, inverse probability weighting) and doubly-robust estimators (augmented inverse probability weighting, targeted maximum likelihood estimation). Nuisance functions were estimated with parametric models and ensemble machine learning, separately. We further assessed cross-fit doubly-robust estimators. With correctly specified parametric models, all of the estimators were unbiased and confidence intervals achieved nominal coverage. When used with machine learning, the cross-fit estimators substantially outperformed all of the other estimators in terms of bias, variance, and confidence interval coverage. Due to the difficulty of properly specifying parametric models in high dimensional data, doubly-robust estimators with ensemble learning and cross-fitting may be the preferred approach for estimation of the ACE in most epidemiologic studies. However, these approaches may require larger sample sizes to avoid finite-sample issues.

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for guiding decisions. However, many interesting models are intractable with standard Bayesian methods, as they lack a closed-form likelihood function or the likelihood is computationally too expensive to evaluate. With this work, we propose a novel method for performing Bayesian model comparison using specialized deep learning architectures. Our method is purely simulation-based and circumvents the step of explicitly fitting all alternative models under consideration to each observed dataset. Moreover, it involves no hand-crafted summary statistics of the data and is designed to amortize the cost of simulation over multiple models and observable datasets. This makes the method applicable in scenarios where model fit needs to be assessed for a large number of datasets, so that per-dataset inference is practically infeasible. Finally, we propose a novel way to measure epistemic uncertainty in model comparison problems. We argue that this measure of epistemic uncertainty provides a unique proxy to quantify absolute evidence even in a framework which assumes that the true data-generating model is within a finite set of candidate models.

The concept of free energy has its origins in 19th century thermodynamics, but has recently found its way into the behavioral and neural sciences, where it has been promoted for its wide applicability and has even been suggested as a fundamental principle of understanding intelligent behavior and brain function. We argue that there are essentially two different notions of free energy in current models of intelligent agency, that can both be considered as applications of Bayesian inference to the problem of action selection: one that appears when trading off accuracy and uncertainty based on a general maximum entropy principle, and one that formulates action selection in terms of minimizing an error measure that quantifies deviations of beliefs and policies from given reference models. The first approach provides a normative rule for action selection in the face of model uncertainty or when information-processing capabilities are limited. The second approach directly aims to formulate the action selection problem as an inference problem in the context of Bayesian brain theories, also known as Active Inference in the literature. We elucidate the main ideas and discuss critical technical and conceptual issues revolving around these two notions of free energy that both claim to apply at all levels of decision-making, from the high-level deliberation of reasoning down to the low-level information-processing of perception.

It is based on the representation of elementary pieces of evidence by belief functions (defined as completely monotone set functions) and on their combination by an operator called the product-intersection rule, or Dempster's rule of combination. A belief function can be constructed by comparing a piece evidence to a scale of canonical examples such as randomly coded messages, whose meanings are determined by chance [40]. A belief function on a set Θ can be seen as being induced by a multi-valued mapping from a probability space to Ω; it is mathematically equivalent to a random set [5, 34]. As rational beliefs are essentially determined by evidence, the Dempster-Shafer (DS) theory can be regarded as a general framework for reasoning with uncertainty [11]. Shortly after the introduction of DS theory, Zadeh independently proposed another formalism, called Possibility Theory [54], in which the concept of "fuzzy restriction" plays a

Papers published at the Neural Information Processing Systems Conference.

Papers published at the Neural Information Processing Systems Conference.