Image modeling with position-encoding dynamic trees

Abstract This paper describes the Position-Encoding Dynamic Tree (PEDT). The PEDT is a probabilistic model for images which improves on the Dynamic Tree by allowing the positions of objects to play a part in the model. This increases the flexibility of the model over the Dynamic Tree and allows the positions of objects to be located and manipulated. The paper motivates and defines this form of probabilistic model using the belief network formalism. A structured variational approach for inference and learning in the PEDT is developed, and the resulting variational updates are obtained, along with additional implementation considerations which ensure the computational cost scales linearly in the number of nodes of the belief network. The PEDT model is demonstrated and compared with the dynamic tree and fixed tree. The structured variational learning method is compared with mean field approaches

Gaussian Process Pseudo-Likelihood Models for Sequence Labeling

Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian processes (GPs) provide a Bayesian approach to learning in a kernel based framework. The pseudo-likelihood model enables one to capture long range dependencies among the output components of the sequence without becoming computationally intractable. We use an efficient variational Gaussian approximation method to perform inference in the proposed model. We also provide an iterative algorithm which can effectively make use of the information from the neighboring labels to perform prediction. The ability to capture long range dependencies makes the proposed approach useful for a wide range of sequence labeling problems. Numerical experiments on some sequence labeling data sets demonstrate the usefulness of the proposed approach.Comment: 18 pages, 5 figure

Bayesian regression filter and the issue of priors

We propose a Bayesian framework for regression problems, which covers areas which are usually dealt with by function approximation. An online learning algorithm is derived which solves regression problems with a Kalman filter. Its solution always improves with increasing model complexity, without the risk of over-fitting. In the infinite dimension limit it approaches the true Bayesian posterior. The issues of prior selection and over-fitting are also discussed, showing that some of the commonly held beliefs are misleading. The practical implementation is summarised. Simulations using 13 popular publicly available data sets are used to demonstrate the method and highlight important issues concerning the choice of priors

Artificial intelligence and machine learning algorithms for early detection of skin cancer in community and primary care settings: a systematic review.

Skin cancers occur commonly worldwide. The prognosis and disease burden are highly dependent on the cancer type and disease stage at diagnosis. We systematically reviewed studies on artificial intelligence and machine learning (AI/ML) algorithms that aim to facilitate the early diagnosis of skin cancers, focusing on their application in primary and community care settings. We searched MEDLINE, Embase, Scopus, and Web of Science (from Jan 1, 2000, to Aug 9, 2021) for all studies providing evidence on applying AI/ML algorithms to the early diagnosis of skin cancer, including all study designs and languages. The primary outcome was diagnostic accuracy of the algorithms for skin cancers. The secondary outcomes included an overview of AI/ML methods, evaluation approaches, cost-effectiveness, and acceptability to patients and clinicians. We identified 14 224 studies. Only two studies used data from clinical settings with a low prevalence of skin cancers. We reported data from all 272 studies that could be relevant in primary care. The primary outcomes showed reasonable mean diagnostic accuracy for melanoma (89·5% [range 59·7-100%]), squamous cell carcinoma (85·3% [71·0-97·8%]), and basal cell carcinoma (87·6% [70·0-99·7%]). The secondary outcomes showed a heterogeneity of AI/ML methods and study designs, with high amounts of incomplete reporting (eg, patient demographics and methods of data collection). Few studies used data on populations with a low prevalence of skin cancers to train and test their algorithms; therefore, the widespread adoption into community and primary care practice cannot currently be recommended until efficacy in these populations is shown. We did not identify any health economic, patient, or clinician acceptability data for any of the included studies. We propose a methodological checklist for use in the development of new AI/ML algorithms to detect skin cancer, to facilitate their design, evaluation, and implementation

Fast algorithms for automatic mapping with space-limited covariance functions

In this paper we discuss a fast Bayesian extension to kriging algorithms which has been used successfully for fast, automatic mapping in emergency conditions in the Spatial Interpolation Comparison 2004 (SIC2004) exercise. The application of kriging to automatic mapping raises several issues such as robustness, scalability, speed and parameter estimation. Various ad-hoc solutions have been proposed and used extensively but they lack a sound theoretical basis. In this paper we show how observations can be projected onto a representative subset of the data, without losing significant information. This allows the complexity of the algorithm to grow as O(n m 2), where n is the total number of observations and m is the size of the subset of the observations retained for prediction. The main contribution of this paper is to further extend this projective method through the application of space-limited covariance functions, which can be used as an alternative to the commonly used covariance models. In many real world applications the correlation between observations essentially vanishes beyond a certain separation distance. Thus it makes sense to use a covariance model that encompasses this belief since this leads to sparse covariance matrices for which optimised sparse matrix techniques can be used. In the presence of extreme values we show that space-limited covariance functions offer an additional benefit, they maintain the smoothness locally but at the same time lead to a more robust, and compact, global model. We show the performance of this technique coupled with the sparse extension to the kriging algorithm on synthetic data and outline a number of computational benefits such an approach brings. To test the relevance to automatic mapping we apply the method to the data used in a recent comparison of interpolation techniques (SIC2004) to map the levels of background ambient gamma radiation. © Springer-Verlag 2007

On the Schoenberg Transformations in Data Analysis: Theory and Illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A simple distance-based discriminant algorithm illustrates the theory, intimately connected to the Gaussian kernels of Machine Learning

Building nonparametric nn-body force fields using Gaussian process regression

Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force fields of a given order using Gaussian process (GP) priors. The formalism of GP regression is first reviewed, particularly in relation to its application in learning local atomic energies and forces. For accurate regression it is fundamental to incorporate prior knowledge into the GP kernel function. To this end, this chapter details how properties of smoothness, invariance and interaction order of a force field can be encoded into corresponding kernel properties. A range of kernels is then proposed, possessing all the required properties and an adjustable parameter $n$ governing the interaction order modelled. The order $n$ best suited to describe a given system can be found automatically within the Bayesian framework by maximisation of the marginal likelihood. The procedure is first tested on a toy model of known interaction and later applied to two real materials described at the DFT level of accuracy. The models automatically selected for the two materials were found to be in agreement with physical intuition. More in general, it was found that lower order (simpler) models should be chosen when the data are not sufficient to resolve more complex interactions. Low $n$ GPs can be further sped up by orders of magnitude by constructing the corresponding tabulated force field, here named "MFF".Comment: 31 pages, 11 figures, book chapte

Genomic analysis of the function of the transcription factor gata3 during development of the Mammalian inner ear

We have studied the function of the zinc finger transcription factor gata3 in auditory system development by analysing temporal profiles of gene expression during differentiation of conditionally immortal cell lines derived to model specific auditory cell types and developmental stages. We tested and applied a novel probabilistic method called the gamma Model for Oligonucleotide Signals to analyse hybridization signals from Affymetrix oligonucleotide arrays. Expression levels estimated by this method correlated closely (p<0.0001) across a 10-fold range with those measured by quantitative RT-PCR for a sample of 61 different genes. In an unbiased list of 26 genes whose temporal profiles clustered most closely with that of gata3 in all cell lines, 10 were linked to Insulin-like Growth Factor signalling, including the serine/threonine kinase Akt/PKB. Knock-down of gata3 in vitro was associated with a decrease in expression of genes linked to IGF-signalling, including IGF1, IGF2 and several IGF-binding proteins. It also led to a small decrease in protein levels of the serine-threonine kinase Akt2/PKB beta, a dramatic increase in Akt1/PKB alpha protein and relocation of Akt1/PKB alpha from the nucleus to the cytoplasm. The cyclin-dependent kinase inhibitor p27(kip1), a known target of PKB/Akt, simultaneously decreased. In heterozygous gata3 null mice the expression of gata3 correlated with high levels of activated Akt/PKB. This functional relationship could explain the diverse function of gata3 during development, the hearing loss associated with gata3 heterozygous null mice and the broader symptoms of human patients with Hearing-Deafness-Renal anomaly syndrome