In this paper, we introduce the use of a personalized Gaussian Process model (pGP) to predict per-patient changes in ADAS-Cog13 -- a significant predictor of Alzheimer's Disease (AD) in the cognitive domain -- using data from each patient's previous visits, and testing on future (held-out) data. We start by learning a population-level model using multi-modal data from previously seen patients using a base Gaussian Process (GP) regression. The personalized GP (pGP) is formed by adapting the base GP sequentially over time to a new (target) patient using domain adaptive GPs. We extend this personalized approach to predict the values of ADAS-Cog13 over the future 6, 12, 18, and 24 months. We compare this approach to a GP model trained only on past data of the target patients (tGP), as well as to a new approach that combines pGP with tGP. We find that the new approach, combining pGP with tGP, leads to large improvements in accurately forecasting future ADAS-Cog13 scores.
However, most of these works attempted forecasting of changes in subjects' CS, which deals with a limited number of future outcomes (i.e., either binary or a three-class). By contrast, we aim to forecast ADAS-Cog13, defined on a more fine-grained scale (85 levels), which poses a more challenging machine learning problem. While in our recent work @cite_21 , we investigated forecasting of ADAS-Cog13 along with other scores (CDSRB, CS, and MMSE), we did so for one step ahead (6 months). In this work, we attempt forecasting of up to 24 months ahead by focusing on ADAS-Cog13.
@cite_21
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Many machine learning and pattern classification methods have been applied to the diagnosis of Alzheimer’s disease (AD) and its prodromal stage, i.e., mild cognitive impairment (MCI). Recently, rather than predicting categorical variables as in classification, several pattern regression methods have also been used to estimate continuous clinical variables from brain images. However, most existing regression methods focus on estimating multiple clinical variables separately and thus cannot utilize the intrinsic useful correlation information among different clinical variables. On the other hand, in those regression methods, only a single modality of data (usually only the structural MRI) is often used, without considering the complementary information that can be provided by different modalities. In this paper, we propose a general methodology, namely Multi-Modal Multi-Task (M3T) learning, to jointly predict multiple variables from multi-modal data. Here, the variables include not only the clinical variables used for regression but also the categorical variable used for classification, with different tasks corresponding to prediction of different variables. Specifically, our method contains two key components, i.e., (1) a multi-task feature selection which selects the common subset of relevant features for multiple variables from each modality, and (2) a multi-modal support vector machine which fuses the above-selected features from all modalities to predict multiple (regression and classification) variables. To validate our method, we perform two sets of experiments on ADNI baseline MRI, FDG-PET, and cerebrospinal fluid (CSF) data from 45 AD patients, 91 MCI patients, and 50 healthy controls (HC). In the first set of experiments, we estimate two clinical variables such as Mini Mental State Examination (MMSE) and Alzheimer’s Disease Assessment Scale - Cognitive Subscale (ADAS-Cog), as well as one categorical variable (with value of ‘AD’, ‘MCI’ or ‘HC’), from the baseline MRI, FDG-PET, and CSF data. In the second set of experiments, we predict the 2-year changes of MMSE and ADAS-Cog scores and also the conversion of MCI to AD from the baseline MRI, FDG-PET, and CSF data. The results on both sets of experiments demonstrate that our proposed M3T learning scheme can achieve better performance on both regression and classification tasks than the conventional learning methods. Reviews studies from 1991-2013 to assess application of ML techniques for SFP.Identifies seven categories of the ML techniques.Identifies 64 studies to answer the established research questions.Selects primary studies according to the quality assessment of the studies.Systematic literature review performs the following:Summarize ML techniques for SFP models.Assess performance accuracy and capability of ML techniques for constructing SFP models.Provide comparison between the ML and statistical techniques.Provide comparison of performance accuracy of different ML techniques.Summarize the strength and weakness of the ML techniques.Provides future guidelines to software practitioners and researchers. BackgroundSoftware fault prediction is the process of developing models that can be used by the software practitioners in the early phases of software development life cycle for detecting faulty constructs such as modules or classes. There are various machine learning techniques used in the past for predicting faults. MethodIn this study we perform a systematic review of studies from January 1991 to October 2013 in the literature that use the machine learning techniques for software fault prediction. We assess the performance capability of the machine learning techniques in existing research for software fault prediction. We also compare the performance of the machine learning techniques with the statistical techniques and other machine learning techniques. Further the strengths and weaknesses of machine learning techniques are summarized. ResultsIn this paper we have identified 64 primary studies and seven categories of the machine learning techniques. The results prove the prediction capability of the machine learning techniques for classifying module class as fault prone or not fault prone. The models using the machine learning techniques for estimating software fault proneness outperform the traditional statistical models. ConclusionBased on the results obtained from the systematic review, we conclude that the machine learning techniques have the ability for predicting software fault proneness and can be used by software practitioners and researchers. However, the application of the machine learning techniques in software fault prediction is still limited and more number of studies should be carried out in order to obtain well formed and generalizable results. We provide future guidelines to practitioners and researchers based on the results obtained in this work. This paper concerns the worst-case complexity of Gauss-Seidel method for solving a positive semi-definite linear system; or equivalently, that of cyclic coordinate descent (C-CD) for minimizing a convex quadratic function. The known provable complexity of C-CD can be @math times slower than gradient descent (GD) and @math times slower than randomized coordinate descent (R-CD). However, these gaps seem rather puzzling since so far they have not been observed in practice; in fact, C-CD usually converges much faster than GD and sometimes comparable to R-CD. Thus some researchers believe the gaps are due to the weakness of the proof, but not that of the C-CD algorithm itself. In this paper we show that the gaps indeed exist. We prove that there exists an example for which C-CD takes at least @math or @math operations, where @math is the condition number, @math is a well-studied quantity that determines the convergence rate of R-CD, and @math hides the dependency on @math . This implies that C-CD can indeed be @math times slower than GD, and @math times slower than R-CD in the worst case. Our result establishes one of the few examples in continuous optimization that demonstrates a large gap between a deterministic algorithm and its randomized counterpart. Based on the example, we establish several almost tight complexity bounds of C-CD for quadratic problems. One difficulty with the analysis of the constructed example is that the spectral radius of a non-symmetric iteration matrix does not necessarily constitutes a lower bound for the convergence rate. By the breakthrough work of Hastad [J ACM 48(4) (2001), 798–859], several constraint satisfaction problems are now known to have the following approximation resistance property: Satisfying more clauses than what picking a random assignment would achieve is NP-hard. This is the case for example for Max E3-Sat, Max E3-Lin, and Max E4-Set Splitting. A notable exception to this extreme hardness is constraint satisfaction over two variables (2-CSP); as a corollary of the celebrated Goemans-Williamson algorithm [J ACM 42(6) (1995), 1115–1145], we know that every Boolean 2-CSP has a nontrivial approximation algorithm whose performance ratio is better than that obtained by picking a random assignment to the variables. An intriguing question then is whether this is also the case for 2-CSPs over larger, non-Boolean domains. This question is still open, and is equivalent to whether the generalization of Max 2-SAT to domains of size d, can be approximated to a factor better than (1 − 1 d2). In an attempt to make progress towards this question, in this paper we prove, first, that a slight restriction of this problem, namely, a generalization of linear inequations with two variables per constraint, is not approximation resistant, and, second, that the Not-All-Equal Sat problem over domain size d with three variables per constraint, is approximation resistant, for every d ≥ 3. In the Boolean case, Not-All-Equal Sat with three variables per constraint is equivalent to Max 2-SAT and thus has a nontrivial approximation algorithm; for larger domain sizes, Max 2-SAT can be reduced to Not-All-Equal Sat with three variables per constraint. Our approximation algorithm implies that a wide class of 2-CSPs called regular 2-CSPs can all be approximated beyond their random assignment threshold. © 2004 Wiley Periodicals, Inc. Random Struct. Alg. 2004