We propose an approach for linear unsupervised dimensionality reduction, based on the sparse linear model that has been used to probabilistically interpret sparse coding. We formulate an optimization problem for learning a linear projection from the original signal domain to a lower-dimensional one in a way that approximately preserves, in expectation, pairwise inner products in the sparse domain. We derive solutions to the problem, present nonlinear extensions, and discuss relations to compressed sensing. Our experiments using facial images, texture patches, and images of object categories suggest that the approach can improve our ability to recover meaningful structure in many classes of signals.

A Bayesian approach to partitioning distance matrices is presented. It is inspired by the Translation-invariant Wishart-Dirichlet process (TIWD) in [1] and shares a number of advantageous properties like the fully probabilistic nature of the inference model, automatic selection of the number of clusters and applicability in semi-supervised settings. In addition, our method (which we call fastTIWD) overcomes the main shortcoming of the original TIWD, namely its high computational costs.

Many functional descriptions of spiking neurons assume a cascade structure where inputs are passed through an initial linear filtering stage that produces a lowdimensional signal that drives subsequent nonlinear stages. This paper presents a novel and systematic parameter estimation procedure for such models and applies the method to two neural estimation problems: (i) compressed-sensing based neural mapping from multi-neuron excitation, and (ii) estimation of neural receptive fields in sensory neurons. The proposed estimation algorithm models the neurons via a graphical model and then estimates the parameters in the model using a recently-developed generalized approximate message passing (GAMP) method. The GAMP method is based on Gaussian approximations of loopy belief propagation. In the neural connectivity problem, the GAMP-based method is shown to be computational efficient, provides a more exact modeling of the sparsity, can incorporate nonlinearities in the output and significantly outperforms previous compressed-sensing methods. For the receptive field estimation, the GAMP method can also exploit inherent structured sparsity in the linear weights. The method is validated on estimation of linear nonlinear Poisson (LNP) cascade models for receptive fields of salamander retinal ganglion cells.

Generalized Linear Models (GLMs) and Single Index Models (SIMs) provide powerful generalizations of linear regression, where the target variable is assumed to be a (possibly unknown) 1-dimensional function of a linear predictor. In general, these problems entail non-convex estimation procedures, and, in practice, iterative local search heuristics are often used. Kalai and Sastry (2009) provided the first provably efficient method, the Isotron algorithm, for learning SIMs and GLMs, under the assumption that the data is in fact generated under a GLM and under certain monotonicity and Lipschitz (bounded slope) constraints.

Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in various scientific and engineering applications, which has motivated the development of reduced-order models (ROMs). Recently, machine-learning-based ROMs have gained significant popularity and are promising for addressing some limitations of traditional ROM methods, especially for advection dominated systems. In this chapter, we focus on a particular framework known as Latent Space Dynamics Identification (LaSDI), which transforms the high-fidelity data, governed by a PDE, to simpler and low-dimensional latent-space data, governed by ordinary differential equations (ODEs). These ODEs can be learned and subsequently interpolated to make ROM predictions. Each building block of LaSDI can be easily modulated depending on the application, which makes the LaSDI framework highly flexible. In particular, we present strategies to enforce the laws of thermodynamics into LaSDI models (tLaSDI), enhance robustness in the presence of noise through the weak form (WLaSDI), select high-fidelity training data efficiently through active learning (gLaSDI, GPLaSDI), and quantify the ROM prediction uncertainty through Gaussian processes (GPLaSDI). We demonstrate the performance of different LaSDI approaches on Burgers equation, a non-linear heat conduction problem, and a plasma physics problem, showing that LaSDI algorithms can achieve relative errors of less than a few percent and up to thousands of times speed-ups.

Alzheimer's Disease (AD) is the most common form of dementia in the United States. Sleep is one of the lifestyle-related factors that has been shown critical for optimal cognitive function in old age. However, there is a lack of research studying the association between sleep and AD incidence. A major bottleneck for conducting such research is that the traditional way to acquire sleep information is time-consuming, inefficient, non-scalable, and limited to patients' subjective experience. A gold standard dataset is created from manual annotation of 570 randomly sampled clinical note documents from the adSLEEP, a corpus of 192,000 de-identified clinical notes of 7,266 AD patients retrieved from the University of Pittsburgh Medical Center (UPMC). We developed a rule-based Natural Language Processing (NLP) algorithm, machine learning models, and Large Language Model(LLM)-based NLP algorithms to automate the extraction of sleep-related concepts, including snoring, napping, sleep problem, bad sleep quality, daytime sleepiness, night wakings, and sleep duration, from the gold standard dataset. Rule-based NLP algorithm achieved the best performance of F1 across all sleep-related concepts. In terms of Positive Predictive Value (PPV), rule-based NLP algorithm achieved 1.00 for daytime sleepiness and sleep duration, machine learning models: 0.95 and for napping, 0.86 for bad sleep quality and 0.90 for snoring; and LLAMA2 with finetuning achieved PPV of 0.93 for Night Wakings, 0.89 for sleep problem, and 1.00 for sleep duration. The results show that the rule-based NLP algorithm consistently achieved the best performance for all sleep concepts. This study focused on the clinical notes of patients with AD, but could be extended to general sleep information extraction for other diseases.

Progress in machine learning (ML) has been fueled by scaling neural network models. This scaling has been enabled by ever more heroic feats of engineering, necessary for accommodating ML approaches that require high bandwidth communication between devices working in parallel. In this work, we propose a co-designed modular architecture and training approach for ML models, dubbed DIstributed PAth COmposition (DiPaCo). During training, DiPaCo distributes computation by paths through a set of shared modules. Together with a Local-SGD inspired optimization (DiLoCo) that keeps modules in sync with drastically reduced communication, Our approach facilitates training across poorly connected and heterogeneous workers, with a design that ensures robustness to worker failures and preemptions. At inference time, only a single path needs to be executed for each input, without the need for any model compression. We consider this approach as a first prototype towards a new paradigm of large-scale learning, one that is less synchronous and more modular. Our experiments on the widely used C4 benchmark show that, for the same amount of training steps but less wall-clock time, DiPaCo exceeds the performance of a 1 billion-parameter dense transformer language model by choosing one of 256 possible paths, each with a size of 150 million parameters.

In this work, we study the out-of-distribution (OOD) detection problem through the use of the feature space of a pre-trained deep classifier. We show that learning the density of in-distribution (ID) features with an energy-based models (EBM) leads to competitive detection results. However, we found that the non-mixing of MCMC sampling during the EBM's training undermines its detection performance. To overcome this an energy-based correction of a mixture of class-conditional Gaussian distributions. We obtains favorable results when compared to a strong baseline like the KNN detector on the CIFAR-10/CIFAR-100 OOD detection benchmarks.

In today's technology-driven era, the imperative for predictive maintenance and advanced diagnostics extends beyond aviation to encompass the identification of damages, failures, and operational defects in rotating and moving machines. Implementing such services not only curtails maintenance costs but also extends machine lifespan, ensuring heightened operational efficiency. Moreover, it serves as a preventive measure against potential accidents or catastrophic events. The advent of Artificial Intelligence (AI) has revolutionized maintenance across industries, enabling more accurate and efficient prediction and analysis of machine failures, thereby conserving time and resources. Our proposed study aims to delve into various machine learning classification techniques, including Support Vector Machine (SVM), Random Forest, Logistic Regression, and Convolutional Neural Network LSTM-Based, for predicting and analyzing machine performance. SVM classifies data into different categories based on their positions in a multidimensional space, while Random Forest employs ensemble learning to create multiple decision trees for classification. Logistic Regression predicts the probability of binary outcomes using input data. The primary objective of the study is to assess these algorithms' performance in predicting and analyzing machine performance, considering factors such as accuracy, precision, recall, and F1 score. The findings will aid maintenance experts in selecting the most suitable machine learning algorithm for effective prediction and analysis of machine performance.

The sheer number of nodes continues to increase in todays supercomputers, the first half of Trinity alone contains more than 9400 compute nodes. Since the speed of todays clusters are limited by the slowest nodes, it more important than ever to identify slow nodes, improve their performance if it can be done, and assure minimal usage of slower nodes during performance critical runs. This is an ongoing maintenance task that occurs on a regular basis and, therefore, it is important to minimize the impact upon its users by assessing and addressing slow performing nodes and mitigating their consequences while minimizing down time. These issues can be solved, in large part, through a systematic application of fast running hardware assessment tests, the application of Machine Learning, and making use of performance data to increase efficiency of large clusters. Proxy applications utilizing both MPI and OpenMP were developed to produce data as a substitute for long runtime applications to evaluate node performance. Machine learning is applied to identify underperforming nodes, and policies are being discussed to both minimize the impact of underperforming nodes and increase the efficiency of the system. In this paper, I will describe the process used to produce quickly performing proxy tests, consider various methods to isolate the outliers, and produce ordered lists for use in scheduling to accomplish this task.