Incremental Sparse Bayesian Ordinal Regression

Ordinal Regression (OR) aims to model the ordering information between different data categories, which is a crucial topic in multi-label learning. An important class of approaches to OR models the problem as a linear combination of basis functions that map features to a high dimensional non-linear space. However, most of the basis function-based algorithms are time consuming. We propose an incremental sparse Bayesian approach to OR tasks and introduce an algorithm to sequentially learn the relevant basis functions in the ordinal scenario. Our method, called Incremental Sparse Bayesian Ordinal Regression (ISBOR), automatically optimizes the hyper-parameters via the type-II maximum likelihood method. By exploiting fast marginal likelihood optimization, ISBOR can avoid big matrix inverses, which is the main bottleneck in applying basis function-based algorithms to OR tasks on large-scale datasets. We show that ISBOR can make accurate predictions with parsimonious basis functions while offering automatic estimates of the prediction uncertainty. Extensive experiments on synthetic and real word datasets demonstrate the efficiency and effectiveness of ISBOR compared to other basis function-based OR approaches

Encrypted statistical machine learning: new privacy preserving methods

We present two new statistical machine learning methods designed to learn on fully homomorphic encrypted (FHE) data. The introduction of FHE schemes following Gentry (2009) opens up the prospect of privacy preserving statistical machine learning analysis and modelling of encrypted data without compromising security constraints. We propose tailored algorithms for applying extremely random forests, involving a new cryptographic stochastic fraction estimator, and na\"{i}ve Bayes, involving a semi-parametric model for the class decision boundary, and show how they can be used to learn and predict from encrypted data. We demonstrate that these techniques perform competitively on a variety of classification data sets and provide detailed information about the computational practicalities of these and other FHE methods.Comment: 39 page

Automated Screening for Three Inborn Metabolic Disorders: A Pilot Study

Background: Inborn metabolic disorders (IMDs) form a large group of rare, but often serious, metabolic disorders. Aims: Our objective was to construct a decision tree, based on classification algorithm for the data on three metabolic disorders, enabling us to take decisions on the screening and clinical diagnosis of a patient. Settings and Design: A non-incremental concept learning classification algorithm was applied to a set of patient data and the procedure followed to obtain a decision on a patient’s disorder. Materials and Methods: Initially a training set containing 13 cases was investigated for three inborn errors of metabolism. Results: A total of thirty test cases were investigated for the three inborn errors of metabolism. The program identified 10 cases with galactosemia, another 10 cases with fructosemia and the remaining 10 with propionic acidemia. The program successfully identified all the 30 cases. Conclusions: This kind of decision support systems can help the healthcare delivery personnel immensely for early screening of IMDs

Separable Convex Optimization with Nested Lower and Upper Constraints

We study a convex resource allocation problem in which lower and upper bounds are imposed on partial sums of allocations. This model is linked to a large range of applications, including production planning, speed optimization, stratified sampling, support vector machines, portfolio management, and telecommunications. We propose an efficient gradient-free divide-and-conquer algorithm, which uses monotonicity arguments to generate valid bounds from the recursive calls, and eliminate linking constraints based on the information from sub-problems. This algorithm does not need strict convexity or differentiability. It produces an $\epsilon$-approximate solution for the continuous problem in $\mathcal{O}(n \log m \log \frac{n B}{\epsilon})$ time and an integer solution in $\mathcal{O}(n \log m \log B)$ time, where $n$ is the number of decision variables, $m$ is the number of constraints, and $B$ is the resource bound. A complexity of $\mathcal{O}(n \log m)$ is also achieved for the linear and quadratic cases. These are the best complexities known to date for this important problem class. Our experimental analyses confirm the good performance of the method, which produces optimal solutions for problems with up to 1,000,000 variables in a few seconds. Promising applications to the support vector ordinal regression problem are also investigated

Earnings Aspirations and Job Satisfaction: The Affective and Cognitive Impact of Earnings Comparisons

Theories of interdependent preferences predicts that the effect of peer earnings on individual well-being is either negative, the “relative deprivation”, or positive the “cognitive effect”. The evidence so far has attributed the dominance of each of the above effects on the country’s economic and political environment. This study claims that relative earnings can affect job satisfaction in two opposite ways, through the affective, “relative deprivation”, and the cognitive channel. The dominance of each effect depends on the individual-specific financial situation rather than the country’s environment. Utilising a longitudinal dataset for British employees, the results of this study show that the cognitive informational effect of “peer earnings” dominates social comparisons for those in financial distress. It further suggests job satisfaction is a relative concept