Forward error correction (FEC) is a key component of modern high-bandwidth networks. Typically implemented at the physical layer, FEC attaches error-correcting codes to blocks of transmitted data, allowing some corrupted blocks to be repaired without retransmission. We outline a synthesis-based approach for automatic exploration of the FEC-code design space, focusing on Hamming codes. We formally verify the correctness of a Hamming (128, 120) code used for FEC in the recent 802.3df Ethernet standard, and provide preliminary evidence that our prototype synthesizer can leverage user-provided formal properties to generate FEC codes that are highly robust, efficiently implementable, and tuned to support specific data formats such as IEEE floating points.

Multi-instance learning (MIL) is an area of machine learning that handles data that is organized into sets of instances known as bags. Traditionally, MIL is used in the supervised-learning setting and is able to classify bags which can contain any number of instances. This property allows MIL to be naturally applied to solve the problems in a wide variety of real-world applications from computer vision to healthcare. However, many traditional MIL algorithms do not scale efficiently to large datasets. In this paper we present a novel Primal-Dual Multi-Instance Support Vector Machine (pdMISVM) derivation and implementation that can operate efficiently on large scale data. Our method relies on an algorithm derived using a multi-block variation of the alternating direction method of multipliers (ADMM). The approach presented in this work is able to scale to large-scale data since it avoids iteratively solving quadratic programming problems which are generally used to optimize MIL algorithms based on SVMs. In addition, we modify our derivation to include an additional optimization designed to avoid solving a least-squares problem during our algorithm; this optimization increases the utility of our approach to handle a large number of features as well as bags. Finally, we apply our approach to synthetic and real-world multi-instance datasets to illustrate the scalability, promising predictive performance, and interpretability of our proposed method. We end our discussion with an extension of our approach to handle non-linear decision boundaries. Code and data for our methods are available online at: https://github.com/minds-mines/pdMISVM.jl.

A critical challenge in using longitudinal neuroimaging data to study the progressions of Alzheimer's Disease (AD) is the varied number of missing records of the patients during the course when AD develops. To tackle this problem, in this paper we propose a novel formulation to learn an enriched representation with fixed length for imaging biomarkers, which aims to simultaneously capture the information conveyed by both baseline neuroimaging record and progressive variations characterized by varied counts of available follow-up records over time. Because the learned biomarker representations are a set of fixedlength vectors, they can be readily used by traditional machine learning models to study AD developments. Take into account that the missing brain scans are not aligned in terms of time in a studied cohort, we develop a new objective that maximizes the ratio of the summations of a number of ℓ1-norm distances for improved robustness, which, though, is difficult to efficiently solve in general. Thus, we derive a new efficient and non-greedy iterative solution algorithm and rigorously prove its convergence. We have performed extensive experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort. A clear performance gain has been achieved in predicting ten different cognitive scores when we compare the original baseline biomarker representations against the learned representations with longitudinal enrichments. We further observe that the top selected biomarkers by our new method are in accordance with known knowledge in AD studies. These promising results have demonstrated improved performances of our new method that validate its effectiveness.

Alzheimer's Disease (AD) is a chronic neurodegenerative disease that severely impacts patients' thinking, memory and behavior. To aid automatic AD diagnoses, many longitudinal learning models have been proposed to predict clinical outcomes and/or disease status, which, though, often fail to consider missing temporal phenotypic records of the patients that can convey valuable information of AD progressions. Another challenge in AD studies is how to integrate heterogeneous genotypic and phenotypic biomarkers to improve diagnosis prediction. To cope with these challenges, in this paper we propose a longitudinal multi-modal method to learn enriched genotypic and phenotypic biomarker representations in the format of fixed-length vectors that can simultaneously capture the baseline neuroimaging measurements of the entire dataset and progressive variations of the varied counts of follow-up measurements over time of every participant from different biomarker sources. The learned global and local projections are aligned by a soft constraint and the structured-sparsity norm is used to uncover the multi-modal structure of heterogeneous biomarker measurements. While the proposed objective is clearly motivated to characterize the progressive information of AD developments, it is a nonsmooth objective that is difficult to efficiently optimize in general. Thus, we derive an efficient iterative algorithm, whose convergence is rigorously guaranteed in mathematics. We have conducted extensive experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) data using one genotypic and two phenotypic biomarkers. Empirical results have demonstrated that the learned enriched biomarker representations are more effective in predicting the outcomes of various cognitive assessments. Moreover, our model has successfully identified disease-relevant biomarkers supported by existing medical findings that additionally warrant the correctness of our method from the clinical perspective.