Many novel unsupervised feature selection methods are proposed each year, yet their empirical evaluation is limited to supervised and unsupervised evaluation metrics computed on selected datasets, along with comparisons to existing methods. However, in the absence of an established evaluation baseline, it is difficult to determine the value added to the existing literature by each of these methods, and how effective their underlying approaches are. We propose using random feature selection as a baseline for evaluating the unsupervised feature selection methods. We empirically show that many of the state-of-the-art methods in unsupervised feature selection are outperformed by random feature selection in both performance and efficiency. Accordingly, we emphasize on the strict requirement of considering random feature selection as a baseline in the development process of novel unsupervised feature selection methods to ensure a consistent improvement over random feature selection.

Fixed-point iteration (FPI) is a crucially important technique at the foundation of many scientific and engineering fields, such as numerical analysis, dynamical systems, optimization, and machine learning. In these domains, algorithmic efficiency and stability is often assessed using the notion of convergence order, a quantity whose estimation has typically involved line fitting in log-log space, or finding the limit of an associated function on differences of sequence values. In this paper, we establish a precise equivalence between the convergence order of a fixed-point update function and the local intrinsic dimensionality (LID) of that function once its fixed point is translated to the origin. Building on this insight, we propose a unified framework for re-purposing existing distributional estimators of LID to estimate the convergence order. Of the LID estimators considered, we show that two, the MLE (Hill) estimator and a Bayesian estimator, have practical and convenient closed-form expressions. We further investigate how these estimators of convergence order can be enhanced using Aitken's Delta(2) method for accelerating convergence in slow scenarios, as well as a Bayesian smoothing layer for reducing variance when the number of samples is small. Empirically, we benchmark our LID-based estimators against classical sequenced-based and curve-fitting methods in three experimental settings: root-finding, general iteration, and machine learning regression. Results indicate that our approaches frequently match or surpass the classical estimators in accuracy, while offering robust performance over a broader range of convergence scenarios.

Local Intrinsic Dimensionality (LID) is a measure of data complexity in the vicinity of a query point. In this work, we propose a novel Bayesian framework for LID estimation that improves robustness and accuracy, especially in scenarios with small neighborhood sizes (k <= 10), where maintaining locality is critical. Our framework allows the incorporation of both informative and non-informative priors, enabling the integration of prior knowledge to enhance the estimation process. Using this framework, we derive new LID estimators and provide insights into transitional ones. Furthermore, we propose aggregation methods using linear and logarithmic pooling to combine multiple LID posteriors. These methods allow for principled integration of LID estimates across different training states of Deep Neural Networks (DNNs), such as epochs, thereby improving estimation stability and performance. We also derive a posterior predictive distribution (PPD) for modeling and synthesizing nearest-neighbor distances. Experiments demonstrate that the LID Bayesian estimation methods achieves a balanced approach between reducing variance and lowering squared bias, often leading to lower mean squared error (MSE) values for small number of nearest neighbors.

The theory of Local Intrinsic Dimensionality (LID) has become a valuable tool for characterizing local complexity within and across data manifolds, supporting a range of data mining and machine learning tasks. Accurate LID estimation requires samples drawn from small neighborhoods around each query to avoid biases from nonlocal effects and potential manifold mixing, yet limited data within such neighborhoods tends to cause high estimation variance. As a variance reduction strategy, we propose an ensemble approach that uses subbagging to preserve the local distribution of nearest neighbor (NN) distances. The main challenge is that the uniform reduction in total sample size within each subsample increases the proximity threshold for finding a fixed number k of NNs around the query. As a result, in the specific context of LID estimation, the sampling rate has an additional, complex interplay with the neighborhood size, where both combined determine the sample size as well as the locality and resolution considered for estimation. We analyze both theoretically and experimentally how the choice of the sampling rate and the k-NN size used for LID estimation, alongside the ensemble size, affects performance, enabling informed prior selection of these hyper-parameters depending on application-based preferences. Our results indicate that within broad and well-characterized regions of the hyper-parameters space, using a bagged estimator will most often significantly reduce variance as well as the mean squared error when compared to the corresponding non-bagged baseline, with controllable impact on bias. We additionally propose and evaluate different ways of combining bagging with neighborhood smoothing for substantial further improvements on LID estimation performance.

The concept of local intrinsic dimensionality (LID) has seen increasing adoption in similarity search and data science. As its use expands, it becomes important to develop new perspectives for interpreting LID, and to clarify its relationships with foundational concepts in statistics and data analysis. In this paper, we examine how LID relates to two key concepts in statistics, degrees of freedom and odds. These connections yield new insights into LID as a measure of dominance over uniformity, and introduce novel analogies for interpreting widely used performance metrics, such as area under the ROC curve and Bayes factors.

Local intrinsic dimensionality (LID) provides insight into the behavior of individual training points in deep neural networks, with applications including adversarial detection, prevention of dimensional collapse in self-supervised learning, and identification of untruthful responses from large language models (LLMs). In such contexts, efficient LID estimation has depended on the use of mini-batches, due to the high cost of computing neighborhoods in latent space. However, estimation with respect to small subsets of the training data usually reflects the dimensionality of the global manifold structure rather than the intended local distribution around each point. In this paper, we propose the Nearest Distance Cache (NDC), a method that improves the locality of LID estimation by reusing nearest-neighbor distances observed in past mini-batches. This strategy faces two key challenges: representations evolve over time, and limited memory prevents storing all past distances. To address these, NDC maintains a compact cache of nearest distances per example and uses window-based change detection to discard outdated samples affected by distributional drift. We also evaluate NDC on two tasks: an autoencoder trained on synthetic data with known ground-truth LID, and a ResNet trained on CIFAR-10. Results show that NDC captures local properties of deep representations not revealed by single mini-batch estimates.

Fixed-point iteration (FPI) is a crucially important technique at the foundation of many scientific and engineering fields, such as numerical analysis, dynamical systems, optimization, and machine learning. In these domains, algorithmic efficiency and stability is often assessed using the notion of convergence order, a quantity whose estimation has typically involved line fitting in log-log space, or finding the limit of an associated function on differences of sequence values. In this paper, we establish a theoretical equivalence between the convergence order of fixed-point iteration and the local intrinsic dimensionality (LID) of the update function as measured from its fixed-point limit. We then show how an existing MLE estimator of LID can be adapted for the context of FPI to produce novel estimators of convergence order, even for those cases where the update function and the limit point of the iteration are unknown. Although most estimators of LID assume that the data samples are drawn from some distribution of distances to a reference point, we show how this assumption can be relaxed using the LID representation theorem. Experiments are provided for a variety of functions that show competitive performance against traditional estimators of convergence order.

Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and modalities. Dimensional collapse also known as the "underfilling" phenomenon is one of the major causes of degraded performance on downstream tasks. Previous work has investigated the dimensional collapse problem of SSL at a global level. In this paper, we demonstrate that representations can span over high dimensional space globally, but collapse locally. To address this, we propose a method called $\textit{local dimensionality regularization (LDReg)}$. Our formulation is based on the derivation of the Fisher-Rao metric to compare and optimize local distance distributions at an asymptotically small radius for each data point. By increasing the local intrinsic dimensionality, we demonstrate through a range of experiments that LDReg improves the representation quality of SSL. The results also show that LDReg can regularize dimensionality at both local and global levels.

Real-time supercomputing performance analysis is a critical aspect of evaluating and optimizing computational systems in a dynamic user environment. The operation of supercomputers produce vast quantities of analytic data from multiple sources and of varying types so compiling this data in an efficient matter is critical to the process. MIT Lincoln Laboratory Supercomputing Center has been utilizing the Unity 3D game engine to create a Digital Twin of our supercomputing systems for several years to perform system monitoring. Unity offers robust visualization capabilities making it ideal for creating a sophisticated representation of the computational processes. As we scale the systems to include a diversity of resources such as accelerators and the addition of more users, we need to implement new analysis tools for the monitoring system. The workloads in research continuously change, as does the capability of Unity, and this allows us to adapt our monitoring tools to scale and incorporate features enabling efficient replay of system wide events, user isolation, and machine level granularity. Our system fully takes advantage of the modern capabilities of the Unity Engine in a way that intuitively represents the real time workload performed on a supercomputer. It allows HPC system engineers to quickly diagnose usage related errors with its responsive user interface which scales efficiently with large data sets.

The MIT/IEEE/Amazon GraphChallenge encourages community approaches to developing new solutions for analyzing graphs and sparse data derived from social media, sensor feeds, and scientific data to discover relationships between events as they unfold in the field. The anonymized network sensing Graph Challenge seeks to enable large, open, community-based approaches to protecting networks. Many large-scale networking problems can only be solved with community access to very broad data sets with the highest regard for privacy and strong community buy-in. Such approaches often require community-based data sharing. In the broader networking community (commercial, federal, and academia) anonymized source-to-destination traffic matrices with standard data sharing agreements have emerged as a data product that can meet many of these requirements. This challenge provides an opportunity to highlight novel approaches for optimizing the construction and analysis of anonymized traffic matrices using over 100 billion network packets derived from the largest Internet telescope in the world (CAIDA). This challenge specifies the anonymization, construction, and analysis of these traffic matrices. A GraphBLAS reference implementation is provided, but the use of GraphBLAS is not required in this Graph Challenge. As with prior Graph Challenges the goal is to provide a well-defined context for demonstrating innovation. Graph Challenge participants are free to select (with accompanying explanation) the Graph Challenge elements that are appropriate for highlighting their innovations.

HPC systems used for research run a wide variety of software and workflows. This software is often written or modified by users to meet the needs of their research projects, and rarely is built with security in mind. In this paper we explore several of the key techniques that MIT Lincoln Laboratory Supercomputing Center has deployed on its systems to manage the security implications of these workflows by providing enforced separation for processes, filesystem access, network traffic, and accelerators to make every user feel like they are running on a personal HPC.

We present a nonparametric method for outlier detection that takes full account of local variations in intrinsic dimensionality within the dataset. Using the theory of Local Intrinsic Dimensionality (LID), our 'dimensionality-aware' outlier detection method, DAO, is derived as an estimator of an asymptotic local expected density ratio involving the query point and a close neighbor drawn at random. The dimensionality-aware behavior of DAO is due to its use of local estimation of LID values in a theoretically-justified way. Through comprehensive experimentation on more than 800 synthetic and real datasets, we show that DAO significantly outperforms three popular and important benchmark outlier detection methods: Local Outlier Factor (LOF), Simplified LOF, and kNN.

Local Intrinsic Dimensionality (LID) is a measure of data complexity in the vicinity of a query point. In this work, we address the problem of estimating LID from a Bayesian perspective by establishing a theoretical framework that derives the distribution of LID given a data sample. Using this framework, we develop new LID estimators that can outperform the Maximum Likelihood Estimator (MLE) in certain contexts. The framework also provides a convenient way to incorporate prior LID knowledge through informative priors. Additionally, we demonstrate how to aggregate multiple LID distributions in a Bayesian manner using logarithmic pooling. We conduct a variety of experiments, demonstrating that a Bayesian approach to LID is effective with a small number of nearest neighbors and when incorporating informative priors. We also show that in deep neural networks, MLE produces highly volatile LID estimates, whereas a Bayesian approach that incorporates prior LID information smoothes and reduces the variance of these estimates.

We present a nonparametric method for outlier detection that takes full account of local variations in intrinsic dimensionality within the dataset. Using the theory of Local Intrinsic Dimensionality (LID), our 'dimensionality-aware' outlier detection method, DAO, is derived as an estimator of an asymptotic local expected density ratio involving the query point and a close neighbor drawn at random. The dimensionality-aware behavior of DAO is due to its use of local estimation of LID values in a theoretically-justified way. Through comprehensive experimentation on more than 800 synthetic and real datasets, we show that DAO significantly outperforms three popular and important benchmark outlier detection methods: Local Outlier Factor (LOF), Simplified LOF, and k NN.

One of the more complex tasks for researchers using HPC systems is performance monitoring and tuning of their applications. Developing a practice of continuous performance improvement, both for speed-up and efficient use of resources is essential to the long term success of both the HPC practitioner and the research project. Profiling tools provide a nice view of the performance of an application but often have a steep learning curve and rarely provide an easy to interpret view of resource utilization. Lower level tools such as top and htop provide a view of resource utilization for those familiar and comfortable with Linux but a barrier for newer HPC practitioners. To expand the existing profiling and job monitoring options, the MIT Lincoln Laboratory Supercomputing Center created LLoad, a tool that captures a snapshot of the resources being used by a job on a per user basis. LLload is a tool built from standard HPC tools that provides an easy way for a researcher to track resource usage of active jobs. We explain how the tool was designed and implemented and provide insight into how it is used to aid new researchers in developing their performance monitoring skills as well as guide researchers in their resource requests.

Hypersparse traffic matrices constructed from network packet source and destination addresses is a powerful tool for gaining insights into network traffic. SuiteSparse: GraphBLAS, an open source package or building, manipulating, and analyzing large hypersparse matrices, is one approach to constructing these traffic matrices. Suricata is a widely used open source network intrusion detection software package. This work demonstrates how Suricata network flow records can be used to efficiently construct hypersparse matrices using GraphBLAS.

There is a tremendous amount of interest in AI/ML technologies due to the proliferation of generative AI applications such as ChatGPT. This trend has significantly increased demand on GPUs, which are the workhorses for training AI models. Due to the high costs of GPUs and lacking supply, it has become of interest to optimize GPU usage in HPC centers. MIT Lincoln Laboratory Supercomputing Center (LLSC) has developed an easy-to-use GPU sharing feature supported by LLSC-developed tools including LLsub and LLMapReduce. This approach overcomes some of the limitations with the existing methods for GPU sharing. This allows users to apply GPU sharing whenever possible while they are developing their AI/ML models and/or doing parametric study on their AI models or executing other GPU applications. Based on our initial experimental results with GPU sharing, GPU sharing with triples mode is easy to use and achieved significant improvement in GPU usage and throughput performance for certain types of AI applications.

The increasing use and cost of high performance computing (HPC) requires new easy-to-use tools to enable HPC users and HPC systems engineers to transparently understand the utilization of resources. The MIT Lincoln Laboratory Supercomputing Center (LLSC) has developed a simple command, LLload, to monitor and characterize HPC workloads. LLload plays an important role in identifying opportunities for better utilization of compute resources. LLload can be used to monitor jobs both programmatically and interactively. LLload can characterize users' jobs using various LLload options to achieve better efficiency. This information can be used to inform the user to optimize HPC workloads and improve both CPU and GPU utilization. This includes improvements using judicious oversubscription of the computing resources. Preliminary results suggest significant improvement in GPU utilization and overall throughput performance with GPU overloading in some cases. By enabling users to observe and fix incorrect job submission and/or inappropriate execution setups, LLload can increase the resource usage and improve the overall throughput performance. LLload is a light-weight, easy-to-use tool for both HPC users and HPC systems engineers to monitor HPC workloads to improve system utilization and efficiency.

Understanding what is normal is a key aspect of protecting a domain. Other domains invest heavily in observational science to develop models of normal behavior to better detect anomalies. Recent advances in high performance graph libraries, such as the GraphBLAS, coupled with supercomputers enables processing of the trillions of observations required. We leverage this approach to synthesize low-parameter observational models of anonymized Internet traffic with a high regard for privacy.

Expanding the scientific tools available to protect computer networks can be aided by a deeper understanding of the underlying statistical distributions of network traffic and their potential geometric interpretations. Analyses of large scale network observations provide a unique window into studying those underlying statistics. Newly developed GraphBLAS hypersparse matrices and D4M associative array technologies enable the efficient anonymized analysis of network traffic on the scale of trillions of events. This work analyzes over 100,000,000,000 anonymized packets from the largest Internet telescope (CAIDA) and over 10,000,000 anonymized sources from the largest commercial honeyfarm (GreyNoise). Neither CAIDA nor GreyNoise actively emit Internet traffic and provide distinct observations of unsolicited Internet traffic (primarily botnets and scanners). Analysis of these observations confirms the previously observed Cauchy-like distributions describing temporal correlations between Internet sources. The Gull lighthouse problem is a well-known geometric characterization of the standard Cauchy distribution and motivates a potential geometric interpretation for Internet observations. This work generalizes the Gull lighthouse problem to accommodate larger classes of coastlines, deriving a closed-form solution for the resulting probability distributions, stating and examining the inverse problem of identifying an appropriate coastline given a continuous probability distribution, identifying a geometric heuristic for solving this problem computationally, and applying that heuristic to examine the temporal geometry of different subsets of network observations. Application of this method to the CAIDA and GreyNoise data reveals a several orders of magnitude difference between known benign and other traffic which can lead to potentially novel ways to protect networks.