The B\"uhlmann model, a branch of classical credibility theory, has been successively applied to the premium estimation for group insurance contracts and other insurance specifications. In this paper, we develop a robust B\"uhlmann credibility via the censored version of loss data, or the censored mean (a robust alternative to traditional individual mean). This framework yields explicit formulas of structural parameters in credibility estimation for both scale-shape distribution families, location-scale distribution families, and their variants, which are commonly used to model insurance risks. The asymptotic properties of the proposed method are provided and corroborated through simulations, and their performance is compared to that of credibility based on the trimmed mean. By varying the censoring/trimming threshold level in several parametric models, we find all structural parameters via censoring are less volatile compared to the corresponding quantities via trimming, and using censored mean as a robust risk measure will reduce the influence of parametric loss assumptions on credibility estimation. Besides, the non-parametric estimations in credibility are discussed using the theory of $L-$estimators. And a numerical illustration from Wisconsin Local Government Property Insurance Fund indicates that the proposed robust credibility can prevent the effect caused by model mis-specification and capture the risk behavior of loss data in a broader viewpoint.
相關內容
A Two-Stage approach is described that literally "straighten outs" any potentially nonlinear relationship between a y-outcome variable and each of p = 2 or more potential x-predictor variables. The y-outcome is then predicted from all p of these "linearized" spline-predictors using the form of Generalized Ridge Regression that is most likely to yield minimal MSE risk under Normal distribution-theory. These estimates are then compared and contrasted with those from the Generalized Additive Model that uses the same x-variables.
One of the most exciting applications of AI is automated scientific discovery based on previously amassed data, coupled with restrictions provided by the known physical principles, including symmetries and conservation laws. Such automated hypothesis creation and verification can assist scientists in studying complex phenomena, where traditional physical intuition may fail. Of particular importance are complex dynamic systems where their time evolution is strongly influenced by varying external parameters. In this paper we develop a platform based on a generalised Onsager principle to learn macroscopic dynamical descriptions of arbitrary stochastic dissipative systems directly from observations of their microscopic trajectories. We focus on systems whose complexity and sheer sizes render complete microscopic description impractical, and constructing theoretical macroscopic models requires extensive domain knowledge or trial-and-error. Our machine learning approach addresses this by simultaneously constructing reduced thermodynamic coordinates and interpreting the dynamics on these coordinates. We demonstrate our method by studying theoretically and validating experimentally, the stretching of long polymer chains in an externally applied field. Specifically, we learn three interpretable thermodynamic coordinates and build a dynamical landscape of polymer stretching, including (1) the identification of stable and transition states and (2) the control of the stretching rate. We further demonstrate the universality of our approach by applying it to an unrelated problem in a different domain: constructing macroscopic dynamics for spatial epidemics, showing that our method addresses wide scientific and technological applications.
Quotient regularization models (QRMs) are a class of powerful regularization techniques that have gained considerable attention in recent years, due to their ability to handle complex and highly nonlinear data sets. However, the nonconvex nature of QRM poses a significant challenge in finding its optimal solution. We are interested in scenarios where both the numerator and the denominator of QRM are absolutely one-homogeneous functions, which is widely applicable in the fields of signal processing and image processing. In this paper, we utilize a gradient flow to minimize such QRM in combination with a quadratic data fidelity term. Our scheme involves solving a convex problem iteratively.The convergence analysis is conducted on a modified scheme in a continuous formulation, showing the convergence to a stationary point. Numerical experiments demonstrate the effectiveness of the proposed algorithm in terms of accuracy, outperforming the state-of-the-art QRM solvers.
The problem of robust hypothesis testing is studied, where under the null and the alternative hypotheses, the data-generating distributions are assumed to be in some uncertainty sets, and the goal is to design a test that performs well under the worst-case distributions over the uncertainty sets. In this paper, uncertainty sets are constructed in a data-driven manner using kernel method, i.e., they are centered around empirical distributions of training samples from the null and alternative hypotheses, respectively; and are constrained via the distance between kernel mean embeddings of distributions in the reproducing kernel Hilbert space, i.e., maximum mean discrepancy (MMD). The Bayesian setting and the Neyman-Pearson setting are investigated. For the Bayesian setting where the goal is to minimize the worst-case error probability, an optimal test is firstly obtained when the alphabet is finite. When the alphabet is infinite, a tractable approximation is proposed to quantify the worst-case average error probability, and a kernel smoothing method is further applied to design test that generalizes to unseen samples. A direct robust kernel test is also proposed and proved to be exponentially consistent. For the Neyman-Pearson setting, where the goal is to minimize the worst-case probability of miss detection subject to a constraint on the worst-case probability of false alarm, an efficient robust kernel test is proposed and is shown to be asymptotically optimal. Numerical results are provided to demonstrate the performance of the proposed robust tests.
Understanding the life cycle of the machine learning (ML) model is an intriguing area of research (e.g., understanding where the model comes from, how it is trained, and how it is used). This paper focuses on a novel problem within this field, namely Model Provenance (MP), which concerns the relationship between a target model and its pre-training model and aims to determine whether a source model serves as the provenance for a target model. This is an important problem that has significant implications for ensuring the security and intellectual property of machine learning models but has not received much attention in the literature. To fill in this gap, we introduce a novel concept of Model DNA which represents the unique characteristics of a machine learning model. We utilize a data-driven and model-driven representation learning method to encode the model's training data and input-output information as a compact and comprehensive representation (i.e., DNA) of the model. Using this model DNA, we develop an efficient framework for model provenance identification, which enables us to identify whether a source model is a pre-training model of a target model. We conduct evaluations on both computer vision and natural language processing tasks using various models, datasets, and scenarios to demonstrate the effectiveness of our approach in accurately identifying model provenance.
Reasoning about the sensitivity of functions with respect to their inputs has interesting applications in various areas, such as differential privacy. In order to check and enforce sensitivity, several approaches have been developed, notably sensitivity type systems. In these systems, sensitivity can be seen as an effect in the sense of type-and-effects systems as originally proposed by Gifford and Lucassen. Because type-and-effect systems can make certain useful programming patterns tedious or overly conservative, there is value in bringing the benefits of gradual typing to these disciplines in order to ease their adoption. In this work, we motivate, formalize, and prototype gradual sensitivity typing. The language GSoul supports both the unrestricted unknown sensitivity and bounded imprecision in the form of intervals. Gradual sensitivity typing allows programmers to smoothly evolve typed programs without any static sensitivity information towards hardened programs with a mix of static and dynamic sensitivity checking. In particular, we show that gradual sensitivity supports recursive functions for which fully static checking would be overly conservative, seamlessly enabling exact runtime sensitivity checks. GSoul satisfies both the gradual guarantees and sensitivity type soundness, known as metric preservation. We establish that, in general, gradual metric preservation is termination insensitive, and that one can achieve termination-sensitive gradual metric preservation by hardening specifications to bounded imprecision. We implement a prototype that provides an interactive test bed for gradual sensitivity typing. This work opens the door to gradualizing other typing disciplines that rely on function sensitivity such as differential privacy, as well as other quantitative type-based reasoning techniques.
The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.
Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.
Attention networks in multimodal learning provide an efficient way to utilize given visual information selectively. However, the computational cost to learn attention distributions for every pair of multimodal input channels is prohibitively expensive. To solve this problem, co-attention builds two separate attention distributions for each modality neglecting the interaction between multimodal inputs. In this paper, we propose bilinear attention networks (BAN) that find bilinear attention distributions to utilize given vision-language information seamlessly. BAN considers bilinear interactions among two groups of input channels, while low-rank bilinear pooling extracts the joint representations for each pair of channels. Furthermore, we propose a variant of multimodal residual networks to exploit eight-attention maps of the BAN efficiently. We quantitatively and qualitatively evaluate our model on visual question answering (VQA 2.0) and Flickr30k Entities datasets, showing that BAN significantly outperforms previous methods and achieves new state-of-the-arts on both datasets.
We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191