-- Th e concordance probability or C - index is a popular measure to capture the discriminatory ability of a regression model. In this article, the definition of this measure is adapted to the specific needs of the frequency and severity model, typically used during the technical pricing of a non - li fe insuran ce product. Due to the typical large sample size of the frequency data in particular, two different adaptations of the estimation procedure of the concordance probability are presented. Note that the latter procedures can be applied to all differ ent versions of the concordance probability . When determining the premium of a non - life insurance product, such as a car insurance product, i ts technical tariff is mostly used as a starting point.

Due to their accuracies, methods based on ensembles of regression trees are a popular approach for making predictions. Some common examples include Bayesian additive regression trees, boosting and random forests. This paper focuses on honest random forests, which add honesty to the original form of random forests and are proved to have better statistical properties. The main contribution is a new method that quantifies the uncertainties of the estimates and predictions produced by honest random forests. The proposed method is based on the generalized fiducial methodology, and provides a fiducial density function that measures how likely each single honest tree is the true model. With such a density function, estimates and predictions, as well as their confidence/prediction intervals, can be obtained. The promising empirical properties of the proposed method are demonstrated by numerical comparisons with several state-of-the-art methods, and by applications to a few real data sets. Lastly, the proposed method is theoretically backed up by a strong asymptotic guarantee.

Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large datasets require to resort to approximations. In this work, the computation of the least-squares prediction is itself treated as a probabilistic inference problem. We propose a structured Gaussian regression model on the kernel function that uses projections of the kernel matrix to obtain a low-rank approximation of the kernel and the matrix. A central result is an enhanced way to use the method of conjugate gradients for the specific setting of least-squares regression as encountered in machine learning. Our method improves the approximation of the kernel ridge regressor / Gaussian process posterior mean over vanilla conjugate gradients and, allows computation of the posterior variance and the log marginal likelihood (evidence) without further overhead.

A BSTRACT In probabilistic classification, a discriminative model based on Gaussian mixture exhibits flexible fitting capability. Nevertheless, it is difficult to determine the number of components. We propose a sparse classifier based on a discriminative Gaussian mixture model (GMM), which is named sparse discriminative Gaussian mixture (SDGM). In the SDGM, a GMM-based discriminative model is trained by sparse Bayesian learning. This learning algorithm improves the generalization capability by obtaining a sparse solution and automatically determines the number of components by removing redundant components. The SDGM can be embedded into neural networks (NNs) such as convolutional NNs and can be trained in an end-to-end manner. Experimental results indicated that the proposed method prevented overfitting by obtaining sparsity. Furthermore, we demonstrated that the proposed method outperformed a fully connected layer with the softmax function in certain cases when it was used as the last layer of a deep NN. 1 I NTRODUCTION In supervised classification, probabilistic classification is an approach that assigns a class label c to an input sample x by estimating the posterior probability P (c x).

The in-depth analysis of time series has gained a lot of research interest in recent years, with the identification of periodic patterns being one important aspect. Many of the methods for identifying periodic patterns require time series' season length as input parameter. There exist only a few algorithms for automatic season length approximation. Many of these rely on simplifications such as data discretization and user defined parameters. This paper presents an algorithm for season length detection that is designed to be sufficiently reliable to be used in practical applications and does not require any input other than the time series to be analyzed. The algorithm estimates a time series' season length by interpolating, filtering and detrending the data. This is followed by analyzing the distances between zeros in the directly corresponding autocorrelation function. Our algorithm was tested against a comparable algorithm and outperformed it by passing 122 out of 165 tests, while the existing algorithm passed 83 tests. The robustness of our method can be jointly attributed to both the algorithmic approach and also to design decisions taken at the implementational level.

This paper proposes a probabilistic neural network developed on the basis of time-series discriminant component analysis (TSDCA) that can be used to classify high-dimensional time-series patterns. TSDCA involves the compression of high-dimensional time series into a lower-dimensional space using a set of orthogonal transformations and the calculation of posterior probabilities based on a continuous-density hidden Markov model with a Gaussian mixture model expressed in the reduced-dimensional space. The analysis can be incorporated into a neural network, which is named a time-series discriminant component network (TSDCN), so that parameters of dimensionality reduction and classification can be obtained simultaneously as network coefficients according to a backpropagation through time-based learning algorithm with the Lagrange multiplier method. The TSDCN is considered to enable high-accuracy classification of high-dimensional time-series patterns and to reduce the computation time taken for network training. The validity of the TSDCN is demonstrated for high-dimensional artificial data and EEG signals in the experiments conducted during the study.

An Application of Multiple-Instance Learning to Estimate Generalization Risk Daiki Suehiro Kyushu University / RIKEN Abstract We focus on several learning approaches that employ max-operator to evaluate the margin. For example, such approaches are commonly used in multi-class learning task and top-rank learning task. In general, in order to estimate the theoretical generalization risk, we need to individually evaluate the complexity of each hypothesis class used in the learning approaches. In this paper, we provide a technique to estimate a theoretical generalization risk for such learning approaches in a same fashion. The key idea is to "redundantly" reformulate the learning problem as one-class multiple-instance learning by redefining the specific input space based on the original input space. Surprisingly, we succeed to improve the generalization risk bounds for some multi-class learning and top-rank learning algorithms. 1 Introduction A lot of margin-based learning approaches such as SVMs have a strong theoretical generalization risk bound and well works in practice. In this paper, we focus on learning approaches that define a margin based on max-operator.

Queen Mary University of London, Imperial College LondonAbstract Sensitive inferences and user re-identification are major threats to privacy when raw sensor data from wearable or portable devices are shared with cloud-assisted applications. To mitigate these threats, we propose mechanisms to transform sensor data before sharing them with applications running on users' devices. These transformations aim at eliminating patterns that can be used for user re-identification or for inferring potentially sensitive activities, while introducing a minor utility loss for the target application (or task). We show that, on gesture and activity recognition tasks, we can prevent inference of potentially sensitive activities while keeping the reduction in recognition accuracy of nonsensitive activities to less than 5 percentage points. We also show that we can reduce the accuracy of user re-identification and of the potential inference of gender to the level of a random guess, while keeping the accuracy of activity recognition comparable to that obtained on the original data.1. Introduction Sensors such as accelerometer, gyroscope, and magnetometer, embedded in personal smart devices generate data that can be used to monitor users' activities, interactions, and mood [1, 2, 3]. Applications (apps) installed on smart devices can get access to raw sensor data to make required(i.e. However, sensor data can also facilitate some potentially sensitive ( i.e. undesired) inferences that a user might wish to keep private, such as discovering smoking habits [4] or revealing personal attributes such as age and gender [5]. Some patterns in raw sensor data may also enable user re-identification [6]. Information privacy can be defined as "the right to select what personal information about me is known to what people" [7].

One key use of k-means clustering is to identify cluster prototypes which can serve as representative points for a dataset. However, a drawback of using k-means cluster centers as representative points is that such points distort the distribution of the underlying data. This can be highly disadvantageous in problems where the representative points are subsequently used to gain insights on the data distribution, as these points do not mimic the distribution of the data. To this end, we propose a new clustering method called "distributional clustering", which ensures cluster centers capture the distribution of the underlying data. We first prove the asymptotic convergence of the proposed cluster centers to the data generating distribution, then present an efficient algorithm for computing these cluster centers in practice. Finally, we demonstrate the effectiveness of distributional clustering on synthetic and real datasets.

Critical task and cognition-based environments, such as in military and defense operations, aviation user-technology interaction evaluation on UI, understanding intuitiveness of a hardware model or software toolkit, etc. require an assessment of how much a particular task is generating mental workload on a user. This is necessary for understanding how those tasks, operations, and activities can be improvised and made better suited for the users so that they reduce the mental workload on the individual and the operators can use them with ease and less difficulty. However, a particular task can be gauged by a user as simple while for others it may be difficult. Understanding the complexity of a particular task can only be done on user level and we propose to do this by understanding the mental workload (MWL) generated on an operator while performing a task which requires processing a lot of information to get the task done. In this work, we have proposed an experimental setup which replicates modern day workload on doing regular day job tasks. We propose an approach to automatically evaluate the task complexity perceived by an individual by using electroencephalogram (EEG) data of a user during operation. Few crucial steps that are addressed in this work include extraction and optimization of different features and selection of relevant features for dimensionality reduction and using supervised machine learning techniques. In addition to this, performance results of the classifiers are compared using all features and also using only the selected features. From the results, it can be inferred that machine learning algorithms perform better as compared to traditional approaches for mental workload estimation.