Cédric Beaulac

Ghazal Mirabnahrazam, Da Ma, Cédric Beaulac et al.

Dementia of Alzheimer's Type (DAT) is a complex disorder influenced by numerous factors, but it is unclear how each factor contributes to disease progression. An in-depth examination of these factors may yield an accurate estimate of time-to-conversion to DAT for patients at various disease stages. We used 401 subjects with 63 features from MRI, genetic, and CDC (Cognitive tests, Demographic, and CSF) data modalities in the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. We used a deep learning-based survival analysis model that extends the classic Cox regression model to predict time-to-conversion to DAT. Our findings showed that genetic features contributed the least to survival analysis, while CDC features contributed the most. Combining MRI and genetic features improved survival prediction over using either modality alone, but adding CDC to any combination of features only worked as well as using only CDC features. Consequently, our study demonstrated that using the current clinical procedure, which includes gathering cognitive test results, can outperform survival analysis results produced using costly genetic or CSF data.

Sidi Wu, Cédric Beaulac, Jiguo Cao

The regression of a functional response on a set of scalar predictors can be a challenging task, especially if there is a large number of predictors, or the relationship between those predictors and the response is nonlinear. In this work, we propose a solution to this problem: a feed-forward neural network (NN) designed to predict a functional response using scalar inputs. First, we transform the functional response to a finite-dimensional representation and construct an NN that outputs this representation. Then, we propose to modify the output of an NN via the objective function and introduce different objective functions for network training. The proposed models are suited for both regularly and irregularly spaced data, and a roughness penalty can be further applied to control the smoothness of the predicted curve. The difficulty in implementing both those features lies in the definition of objective functions that can be back-propagated. In our experiments, we demonstrate that our model outperforms the conventional function-on-scalar regression model in multiple scenarios while computationally scaling better with the dimension of the predictors.

Cédric Beaulac, Sidi Wu, Erin Gibson et al.

A major issue in the association of genes to neuroimaging phenotypes is the high dimension of both genetic data and neuroimaging data. In this article, we tackle the latter problem with an eye toward developing solutions that are relevant for disease prediction. Supported by a vast literature on the predictive power of neural networks, our proposed solution uses neural networks to extract from neuroimaging data features that are relevant for predicting Alzheimer's Disease (AD) for subsequent relation to genetics. Our neuroimaging-genetic pipeline is comprised of image processing, neuroimaging feature extraction and genetic association steps. We propose a neural network classifier for extracting neuroimaging features that are related with disease and a multivariate Bayesian group sparse regression model for genetic association. We compare the predictive power of these features to expert selected features and take a closer look at the SNPs identified with the new neuroimaging features.

Sidi Wu, Cédric Beaulac, Jiguo Cao

A common pipeline in functional data analysis is to first convert the discretely observed data to smooth functions, and then represent the functions by a finite-dimensional vector of coefficients summarizing the information. Existing methods for data smoothing and dimensional reduction mainly focus on learning the linear mappings from the data space to the representation space, however, learning only the linear representations may not be sufficient. In this study, we propose to learn the nonlinear representations of functional data using neural network autoencoders designed to process data in the form it is usually collected without the need of preprocessing. We design the encoder to employ a projection layer computing the weighted inner product of the functional data and functional weights over the observed timestamp, and the decoder to apply a recovery layer that maps the finite-dimensional vector extracted from the functional data back to functional space using a set of predetermined basis functions. The developed architecture can accommodate both regularly and irregularly spaced data. Our experiments demonstrate that the proposed method outperforms functional principal component analysis in terms of prediction and classification, and maintains superior smoothing ability and better computational efficiency in comparison to the conventional autoencoders under both linear and nonlinear settings.

Issam-Ali Moindjié, Marie-Hélène Descary, Cédric Beaulac

Recent developments in computer vision have enabled the availability of segmented images across various domains, such as medicine, where segmented radiography images play an important role in diagnosis-making. As prediction problems are common in medical image analysis, this work explores the use of segmented images (through the associated contours they highlight) as predictors in a supervised classification context. Consequently, we develop a new approach for image analysis that takes into account the shape of objects within images. For this aim, we introduce a new formalism that extends the study of single random planar curves to the joint analysis of multiple planar curves-referred to here as multivariate planar curves. In this framework, we propose a solution to the alignment issue in statistical shape analysis. The obtained multivariate shape variables are then used in functional classification methods through tangent projections. Detection of cardiomegaly in segmented X-rays and numerical experiments on synthetic data demonstrate the appeal and robustness of the proposed method.

Mélanie Raymond, Marie-Hélène Descary, Cédric Beaulac et al.

Over the years, many approaches have been proposed to build ancestral recombination graphs (ARGs), graphs used to represent the genetic relationship between individuals. Among these methods, many rely on the assumption that the most likely graph is among the shortest ones. In this paper, we propose a new approach to build short ARGs: Reinforcement Learning (RL). We exploit the similarities between finding the shortest path between a set of genetic sequences and their most recent common ancestor and finding the shortest path between the entrance and exit of a maze, a classic RL problem. In the maze problem, the learner, called the agent, must learn the directions to take in order to escape as quickly as possible, whereas in our problem, the agent must learn the actions to take between coalescence, mutation, and recombination in order to reach the most recent common ancestor as quickly as possible. Our results show that RL can be used to build ARGs as short as those built with a heuristic algorithm optimized to build short ARGs, and sometimes even shorter. Moreover, our method allows to build a distribution of short ARGs for a given sample, and can also generalize learning to new samples not used during the learning process.

Cédric Beaulac

It can be difficult to assess the quality of a fitted model when facing unsupervised learning problems. Latent variable models, such as variation autoencoders and Gaussian mixture models, are often trained with likelihood-based approaches. In scope of Goodhart's law, when a metric becomes a target it ceases to be a good metric and therefore we should not use likelihood to assess the quality of the fit of these models. The solution we propose is a new metric for model comparison or regularization that relies on moments. The concept is to study the difference between the data moments and the model moments using a matrix norm, such as the Frobenius norm. We show how to use this new metric for model comparison and then for regularization. It is common to draw samples from the fitted distribution when evaluating latent variable models and we show that our proposed metric is faster to compute and has a smaller variance that this alternative. We conclude this article with a proof of concept of both applications and we discuss future work.

Cédric Beaulac, Jeffrey S. Rosenthal

The contributions in this article are two-fold. First, we introduce a new hand-written digit data set that we collected. It contains high-resolution images of hand-written The contributions in this article are two-fold. First, we introduce a new handwritten digit data set that we collected. It contains high-resolution images of handwritten digits together with various writer characteristics which are not available in the well-known MNIST database. The multiple writer characteristics gathered are a novelty of our data set and create new research opportunities. The data set is publicly available online. Second, we analyse this new data set. We begin with simple supervised tasks. We assess the predictability of the writer characteristics gathered, the effect of using some of those characteristics as predictors in classification task and the effect of higher resolution images on classification accuracy. We also explore semi-supervised applications; we can leverage the high quantity of handwritten digits data sets already existing online to improve the accuracy of various classifications task with noticeable success. Finally, we also demonstrate the generative perspective offered by this new data set; we are able to generate images that mimics the writing style of specific writers. The data set has unique and distinct features and our analysis establishes benchmarks and showcases some of the new opportunities made possible with this new data set.

Cédric Beaulac, Jeffrey S. Rosenthal, Qinglin Pei et al.

In this manuscript we analyze a data set containing information on children with Hodgkin Lymphoma (HL) enrolled on a clinical trial. Treatments received and survival status were collected together with other covariates such as demographics and clinical measurements. Our main task is to explore the potential of machine learning (ML) algorithms in a survival analysis context in order to improve over the Cox Proportional Hazard (CoxPH) model. We discuss the weaknesses of the CoxPH model we would like to improve upon and then we introduce multiple algorithms, from well-established ones to state-of-the-art models, that solve these issues. We then compare every model according to the concordance index and the brier score. Finally, we produce a series of recommendations, based on our experience, for practitioners that would like to benefit from the recent advances in artificial intelligence.

Cédric Beaulac, Jeffrey S. Rosenthal, David Hodgson

In the following short article we adapt a new and popular machine learning model for inference on medical data sets. Our method is based on the Variational AutoEncoder (VAE) framework that we adapt to survival analysis on small data sets with missing values. In our model, the true health status appears as a set of latent variables that affects the observed covariates and the survival chances. We show that this flexible model allows insightful decision-making using a predicted distribution and outperforms a classic survival analysis model.

Cédric Beaulac, Jeffrey S. Rosenthal

The main contribution of this paper is the development of a new decision tree algorithm. The proposed approach allows users to guide the algorithm through the data partitioning process. We believe this feature has many applications but in this paper we demonstrate how to utilize this algorithm to analyse data sets containing missing values. We tested our algorithm against simulated data sets with various missing data structures and a real data set. The results demonstrate that this new classification procedure efficiently handles missing values and produces results that are slightly more accurate and more interpretable than most common procedures without any imputations or pre-processing.

Cédric Beaulac, Jeffrey S. Rosenthal

In this article, a large data set containing every course taken by every undergraduate student in a major university in Canada over 10 years is analysed. Modern machine learning algorithms can use large data sets to build useful tools for the data provider, in this case, the university. In this article, two classifiers are constructed using random forests. To begin, the first two semesters of courses completed by a student are used to predict if they will obtain an undergraduate degree. Secondly, for the students that completed a program, their major is predicted using once again the first few courses they have registered to. A classification tree is an intuitive and powerful classifier and building a random forest of trees improves this classifier. Random forests also allow for reliable variable importance measurements. These measures explain what variables are useful to the classifiers and can be used to better understand what is statistically related to the students' situation. The results are two accurate classifiers and a variable importance analysis that provides useful information to university administrations.

Cédric Beaulac, Fabrice Larribe

We propose to use a supervised machine learning technique to track the location of a mobile agent in real time. Hidden Markov Models are used to build artificial intelligence that estimates the unknown position of a mobile target moving in a defined environment. This narrow artificial intelligence performs two distinct tasks. First, it provides real-time estimation of the mobile agent's position using the forward algorithm. Second, it uses the Baum-Welch algorithm as a statistical learning tool to gain knowledge of the mobile target. Finally, an experimental environment is proposed, namely a video game that we use to test our artificial intelligence. We present statistical and graphical results to illustrate the efficiency of our method.