The Bayesian evidence framework is applied in this paper to least squares support vector machine (LS-SVM) regression in order to infer nonlinear models for predicting a financial time series and the related volatility. On the first level of inference, a statistical framework is related to the LS-SVM formulation which allows one to include the time-varying volatility of the market by an appropriate choice of several hyper-parameters. The hyper-parameters of the model are inferred on the second level of inference. The inferred hyper-parameters, related to the volatility, are used to construct a volatility model within the evidence framework. Model comparison is performed on the third level of inference in order to automatically tune the parameters of the kernel function and to select the relevant inputs. The LS-SVM formulation allows one to derive analytic expressions in the feature space and practical expressions are obtained in the dual space replacing the inner product by the related kernel function using Mercer's theorem. The one step ahead prediction performances obtained on the prediction of the weekly 90-day T-bill rate and the daily DAX30 closing prices show that significant out of sample sign predictions can be made with respect to the Pesaran-Timmerman test statistic.

The Bayesian evidence framework has been successfully applied to the design of multilayer perceptrons (MLPs) in the work of MacKay. Nevertheless, the training of MLPs suffers from drawbacks like the nonconvex optimization problem and the choice of the number of hidden units. In support vector machines (SVMs) for classification, as introduced by Vapnik, a nonlinear decision boundary is obtained by mapping the input vector first in a nonlinear way to a high-dimensional kernel-induced feature space in which a linear large margin classifier is constructed. Practical expressions are formulated in the dual space in terms of the related kernel function, and the solution follows from a (convex) quadratic programming (QP) problem. In least-squares SVMs (LS-SVMs), the SVM problem formulation is modified by introducing a least-squares cost function and equality instead of inequality constraints, and the solution follows from a linear system in the dual space. Implicitly, the least-squares formulation corresponds to a regression formulation and is also related to kernel Fisher discriminant analysis. The least-squares regression formulation has advantages for deriving analytic expressions in a Bayesian evidence framework, in contrast to the classification formulations used, for example, in gaussian processes (GPs). The LS-SVM formulation has clear primal-dual interpretations, and without the bias term, one explicitly constructs a model that yields the same expressions as have been obtained with GPs for regression. In this article, the Bayesian evidence framework is combined with the LS-SVM classifier formulation. Starting from the feature space formulation, analytic expressions are obtained in the dual space on the different levels of Bayesian inference, while posterior class probabilities are obtained by marginalizing over the model parameters. Empirical results obtained on 10 public domain data sets show that the LS-SVM classifier designed within the Bayesian evidence framework consistently yields good generalization performances.

Previous studies have shown that the manufacturer’s default preoperative plans for total knee arthroplasty with patient-specific guides require frequent, time-consuming changes by the surgeon. Currently, no research has been done on predicting preoperative plans for orthopedic surgery using machine learning. Therefore, this study aims to evaluate whether artificial intelligence (AI) driven planning tools can create surgeon and patient-specific preoperative plans that require fewer changes by the surgeon. A dataset of 5409 preoperative plans, including the manufacturer’s default and the plans corrected by 39 surgeons, was collected. Features were extracted from the preoperative plans that describe the implant sizes, position, and orientation in a surgeon- and patient-specific manner. Based on these features, non-linear regression models were employed to predict the surgeon’s corrected preoperative plan. The average number of corrections a surgeon has to make to the preoperative plan generated using AI was reduced by 39.7% compared to the manufacturer’s default plan. The femoral and tibial implant size in the manufacturer’s plan was correct in 68.4% and 73.1% of the cases, respectively, while the AI-based plan was correct in 82.2% and 85.0% of the cases, respectively, compared to the surgeon approved plan. Our method successfully demonstrated the use of machine learning to create preoperative plans in a surgeon- and patient-specific manner for total knee arthroplasty.

A preoperative plan is a virtual plan that defines the implant position and orientation allowing a surgeon to prepare for surgery. However, the default preoperative plan for total knee arthroplasty proposed by the manufacturer requires changes to be made by the surgeon in more than 90% of the cases. Previous studies have shown that artificial intelligence can be used to create better preoperative plans compared to manufacturer’s default plans. However, the quality of artificial intelligence based preoperative plans has not yet been compared to surgeon approved preoperative plans. The purpose of this study is to compare default, artificial intelligence and surgeon approved preoperative plans, by having them scored on a range from 1 (totally unacceptable plan) to 5 (no corrections needed) by an experienced surgeon, while being blinded to the plan type. Through a Wilcoxon signed rank test with α=0.05, AI based preoperative plans were found to be a significant improvement upon the default plans (p-val=0.000136), while the differences in score between AI and surgeon approved preoperative plans were insignificant (p-val= 0.083). Consequently these results indicate that AI generated preoperative plans for TKA are an improvement upon current default plans, which could increase the surgeon’s planning efficiency when applied in clinical practice.