This study explores a Bayesian algorithmic approach to personalized fragrance recommendation by integrating hierarchical Relevance Vector Machines (RVM) and Jungian personality archetypes. The paper proposes a structured model that links individual scent preferences for top, middle, and base notes to personality traits derived from Jungian archetypes, such as the Hero, Caregiver, and Explorer, among others. The algorithm utilizes Bayesian updating to dynamically refine predictions as users interact with each fragrance note. This iterative process allows for the personalization of fragrance experiences based on prior data and personality assessments, leading to adaptive and interpretable recommendations. By combining psychological theory with Bayesian machine learning, this approach addresses the complexity of modeling individual preferences while capturing user-specific and population-level trends. The study highlights the potential of hierarchical Bayesian frameworks in creating customized olfactory experiences, informed by psychological and demographic factors, contributing to advancements in personalized product design and machine learning applications in sensory-based industries.

The support vector machine (SVM) is a state-of-the-art technique for regression and classification, combining excellent generalisation properties with a sparse kernel representation. However, it does suffer from a number of disadvantages, notably the absence of prob(cid:173) abilistic outputs, the requirement to estimate a trade-off parameter and the need to utilise'Mercer' kernel functions. In this paper we introduce the Relevance Vector Machine (RVM), a Bayesian treat(cid:173) ment of a generalised linear model of identical functional form to the SVM. The RVM suffers from none of the above disadvantages, and examples demonstrate that for comparable generalisation per(cid:173) formance, the RVM requires dramatically fewer kernel functions.

Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. Chakraborty et al. (2012) did a full hierarchical Bayesian analysis of nonlinear regression in such situations using relevance vector machines based on reproducing kernel Hilbert space (RKHS). But they did not provide any theoretical properties associated with their procedure. The present paper revisits their problem, introduces a new class of global-local priors different from theirs, and provides results on posterior consistency as well as posterior contraction rates.

The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and interpretability via uncertainty analysis. This article introduces and discusses two methods which straddle the areas of probabilistic Bayesian schemes and kernel methods for regression: Gaussian Processes and Relevance Vector Machines. Our focus is on developing a common framework with which to view these methods, via intermediate methods a probabilistic version of the well-known kernel ridge regression, and drawing connections among them, via dual formulations, and discussion of their application in the context of major tasks: regression, smoothing, interpolation, and filtering. Overall, we provide understanding of the mathematical concepts behind these models, and we summarize and discuss in depth different interpretations and highlight the relationship to other methods, such as linear kernel smoothers, Kalman filtering and Fourier approximations. Throughout, we provide numerous figures to promote understanding, and we make numerous recommendations to practitioners. Benefits and drawbacks of the different techniques are highlighted. To our knowledge, this is the most in-depth study of its kind to date focused on these two methods, and will be relevant to theoretical understanding and practitioners throughout the domains of data-science, signal processing, machine learning, and artificial intelligence in general.

In the variational relevance vector machine, the gamma distribution is representative as a hyperprior over the noise precision of automatic relevance determination prior. Instead of the gamma hyperprior, we propose to use the inverse gamma hyperprior with a shape parameter close to zero and a scale parameter not necessary close to zero. This hyperprior is associated with the concept of a weakly informative prior. The effect of this hyperprior is investigated through regression to non-homogeneous data. Because it is difficult to capture the structure of such data with a single kernel function, we apply the multiple kernel method, in which multiple kernel functions with different widths are arranged for input data. We confirm that the degrees of freedom in a model is controlled by adjusting the scale parameter and keeping the shape parameter close to zero. A candidate for selecting the scale parameter is the predictive information criterion. However the estimated model using this criterion seems to cause over-fitting. This is because the multiple kernel method makes the model a situation where the dimension of the model is larger than the data size. To select an appropriate scale parameter even in such a situation, we also propose an extended prediction information criterion. It is confirmed that a multiple kernel relevance vector regression model with good predictive accuracy can be obtained by selecting the scale parameter minimizing extended prediction information criterion.

With the increased need for multi-center magnetic resonance imaging studies, problems arise related to differences in hardware and software between centers. Namely, current algorithms for brain volume quantification are unreliable for the longitudinal assessment of volume changes in this type of setting. Currently most methods attempt to decrease this issue by regressing the scanner- and/or center-effects from the original data. In this work, we explore a novel approach to harmonize brain volume measurements by using only image descriptors. First, we explore the relationships between volumes and image descriptors. Then, we train a Relevance Vector Machine (RVM) model over a large multi-site dataset of healthy subjects to perform volume harmonization. Finally, we validate the method over two different datasets: i) a subset of unseen healthy controls; and ii) a test-retest dataset of multiple sclerosis (MS) patients. The method decreases scanner and center variability while preserving measurements that did not require correction in MS patient data. We show that image descriptors can be used as input to a machine learning algorithm to improve the reliability of longitudinal volumetric studies.

Pattern recognition and machine learning are becoming integral parts of algorithms in a wide range of applications. Different algorithms and approaches for machine learning include different tradeoffs between performance and computation, so during algorithm development it is often necessary to explore a variety of different approaches to a given task. A toolbox with a unified framework across multiple pattern recognition techniques enables algorithm developers the ability to rapidly evaluate different choices prior to deployment. MATLAB is a widely used environment for algorithm development and prototyping, and although several MATLAB toolboxes for pattern recognition are currently available these are either incomplete, expensive, or restrictively licensed. In this work we describe a MATLAB toolbox for pattern recognition and machine learning known as the PRT (Pattern Recognition Toolbox), licensed under the permissive MIT license. The PRT includes many popular techniques for data preprocessing, supervised learning, clustering, regression and feature selection, as well as a methodology for combining these components using a simple, uniform syntax. The resulting algorithms can be evaluated using cross-validation and a variety of scoring metrics to ensure robust performance when the algorithm is deployed. This paper presents an overview of the PRT as well as an example of usage on Fisher's Iris dataset.

The Support Vector Machine (SVM) of Vapnik (1998) has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions centred on a subset of the training data, known as support vectors. Despite its widespread success, the SVM suffers from some important limitations, one of the most significant being that it makes point predictions rather than generating predictive distributions. Recently Tipping (1999) has formulated the Relevance Vector Machine (RVM), a probabilistic model whose functional form is equivalent to the SVM. It achieves comparable recognition accuracy to the SVM, yet provides a full predictive distribution, and also requires substantially fewer kernel functions. The original treatment of the RVM relied on the use of type II maximum likelihood (the `evidence framework') to provide point estimates of the hyperparameters which govern model sparsity. In this paper we show how the RVM can be formulated and solved within a completely Bayesian paradigm through the use of variational inference, thereby giving a posterior distribution over both parameters and hyperparameters. We demonstrate the practicality and performance of the variational RVM using both synthetic and real world examples.

In this work we present an advanced Bayesian formulation to the task of control learning that employs the Relevance Vector Machines (RVM) generative model for value function evaluation. The key aspect of the proposed method is the design of the discount return as a generalized linear model that constitutes a well-known probabilistic approach. This allows to augment the model with advantageous sparse priors provided by the RVM's regression framework. We have also taken into account the significant issue of selecting the proper parameters of the kernel design matrix. Experiments have shown that our method produces improved performance in both simulated and real test environments.

Recently, relevance vector machines (RVM) have been fashioned from a sparse Bayesian learning (SBL) framework to perform supervised learning usinga weight prior that encourages sparsity of representation. The methodology incorporates an additional set of hyperparameters governing theprior, one for each weight, and then adopts a specific approximation tothe full marginalization over all weights and hyperparameters. Despite its empirical success however, no rigorous motivation for this particular approximation is currently available. To address this issue, we demonstrate that SBL can be recast as the application of a rigorous variational approximationto the full model by expressing the prior in a dual form. This formulation obviates the necessity of assuming any hyperpriors andleads to natural, intuitive explanations of why sparsity is achieved in practice.