To learn intrinsic low-dimensional structures from high-dimensional data that most discriminate between classes, we propose the principle of Maximal Coding Rate Reduction ($\text{MCR}^2$), an information-theoretic measure that maximizes the coding rate difference between the whole dataset and the sum of each individual class. We clarify its relationships with most existing frameworks such as cross-entropy, information bottleneck, information gain, contractive and contrastive learning, and provide theoretical guarantees for learning diverse and discriminative features. The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner. Empirically, the representations learned using this principle alone are significantly more robust to label corruptions in classification than those using cross-entropy, and can lead to state-of-the-art results in clustering mixed data from self-learned invariant features.

The broader ambition of this article is to popularize an approach for the fair distribution of the quantity of a system's output to its subsystems, while allowing for underlying complex subsystem level interactions. Particularly, we present a data-driven approach to vehicle price modeling and its component price estimation by leveraging a combination of concepts from machine learning and game theory. We show an alternative to common teardown methodologies and surveying approaches for component and vehicle price estimation at the manufacturer's suggested retail price (MSRP) level that has the advantage of bypassing the uncertainties involved in 1) the gathering of teardown data, 2) the need to perform expensive and biased surveying, and 3) the need to perform retail price equivalent (RPE) or indirect cost multiplier (ICM) adjustments to mark up direct manufacturing costs to MSRP. This novel exercise not only provides accurate pricing of the technologies at the customer level, but also shows the, a priori known, large gaps in pricing strategies between manufacturers, vehicle sizes, classes, market segments, and other factors. There is also clear synergism or interaction between the price of certain technologies and other specifications present in the same vehicle. Those (unsurprising) results are indication that old methods of manufacturer-level component costing, aggregation, and the application of a flat and rigid RPE or ICM adjustment factor should be carefully examined. The findings are based on an extensive database, developed by Argonne National Laboratory, that includes more than 64,000 vehicles covering MY1990 to MY2020 over hundreds of vehicle specs.

In this work we solve the Dynamic Vehicle Routing Problem (DVRP). DVRP is a modification of the Vehicle Routing Problem, in which the clients' requests (cities) number and location might not be known at the beginning of the working day Additionally, all requests must be served during one working day by a fleet of vehicles with limited capacity. In this work we propose a Monte Carlo method (MCTree), which directly approaches the dynamic nature of arriving requests in the DVRP. The method is also hybridized (MCTree+PSO) with our previous Two-Phase Multi-swarm Particle Swarm Optimization (2MPSO) algorithm. Our method is based on two assumptions. First, that we know a bounding rectangle of the area in which the requests might appear. Second, that the initial requests' sizes and frequency of appearance are representative for the yet unknown clients' requests. In order to solve the DVRP we divide the working day into several time slices in which we solve a static problem. In our Monte Carlo approach we randomly generate the unknown clients' requests with uniform spatial distribution over the bounding rectangle and requests' sizes uniformly sampled from the already known requests' sizes. The solution proposal is constructed with the application of a clustering algorithm and a route construction algorithm. The MCTree method is tested on a well established set of benchmarks proposed by Kilby et al. and is compared with the results achieved by applying our previous 2MPSO algorithm and other literature results. The proposed MCTree approach achieves a better time to quality trade-off then plain heuristic algorithms. Moreover, a hybrid MCTree+PSO approach achieves better time to quality trade-off then 2MPSO for small optimization time limits, making the hybrid a good candidate for handling real world scale goods delivery problems.

Clustering and prediction are two primary tasks in the fields of unsupervised and supervised learning, respectively. Although much of the recent advances in machine learning have been centered around those two tasks, the interdependent, mutually beneficial relationship between them is rarely explored. One could reasonably expect appropriately clustering the data would aid the downstream prediction task and, conversely, a better prediction performance for the downstream task could potentially inform a more appropriate clustering strategy. In this work, we focus on the latter part of this mutually beneficial relationship. To this end, we introduce Deep Goal-Oriented Clustering (DGC), a probabilistic framework that clusters the data by jointly using supervision via side-information and unsupervised modeling of the inherent data structure in an end-to-end fashion. We show the effectiveness of our model on a range of datasets by achieving prediction accuracies comparable to the state-of-the-art, while, more importantly in our setting, simultaneously learning congruent clustering strategies.

Two examples of anomaly detection based on MDL have been been proposed for categorical data based on the minimum description studied and shown to perform well: the OC3 algorithm [21] based length (MDL) principle. However, they can be ineffective when on an itemset mining technique called Krimp [26], and the CompreX detecting anomalies in heterogeneous datasets representing a mixture algorithm [2]. Broadly speaking, both take a similar approach: of different sources, such as security scenarios in which system first, a model H of the data that compresses it well is found using a and user processes have distinct behavior patterns. We propose a heuristic search, balancing the model complexity L(H) (number of meta-algorithm for enhancing any MDL-based anomaly detection bits required to compress the model structure/parameters) against model to deal with heterogeneous data by fitting a mixture model the data complexity L(X H) (number of bits required to compress to the data, via a variant of k-means clustering. Our experimental the data given the model). Once such a model H is found, we assign results show that using a discrete mixture model provides competitive to each object x X a score corresponding to the object's performance relative to two previous anomaly detection compressed size L(x H) given the selected model. Intuitively, if the algorithms, while mixtures of more sophisticated models yield further model accurately characterizes the data as a whole, records that are gains, on both synthetic datasets and realistic datasets from a representative will compress well, yielding a low anomaly score, security scenario.

Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap. This work proposes an algorithm that consistently estimates any identifiable mixture model from grouped observations. Our analysis leverages an oracle inequality for weighted kernel density estimators of the distribution on groups, together with a general result showing that consistent estimation of the distribution on groups implies consistent estimation of mixture components. A practical implementation is provided for paired observations, and the approach is shown to outperform existing methods, especially when mixture components overlap significantly.

We introduce Markov Random Geometric Graphs (MRGGs), a growth model for temporal dynamic networks. It is based on a Markovian latent space dynamic: consecutive latent points are sampled on the Euclidean Sphere using an unknown Markov kernel; and two nodes are connected with a probability depending on a unknown function of their latent geodesic distance. More precisely, at each stamp-time k we add a latent point X k sampled by jumping from the previous one X k--1 in a direction chosen uniformly Y k and with a length r k drawn from an unknown distribution called the latitude function. The connection probabilities between each pair of nodes are equal to the envelope function of the distance between these two latent points. We provide theoretical guarantees for the non-parametric estimation of the latitude and the envelope functions. We propose an efficient algorithm that achieves those non-parametric estimation tasks based on an ad-hoc Hierarchical Agglomerative Clustering approach, and we deploy this analysis on a real data-set given by exchange of messages on a social network.

Achieving statistically significant evaluation with passive sampling of test data is challenging in settings such as extreme classification and record linkage, where significant class imbalance is prevalent. Adaptive importance sampling focuses labeling on informative regions of the instance space, however it breaks data independence assumptions - commonly required for asymptotic guarantees that assure estimates approximate population performance and provide practical confidence intervals. In this paper we develop an adaptive importance sampling framework for supervised evaluation that defines a sequence of proposal distributions given a user-defined discriminative model of p(y|x) and a generalized performance measure to evaluate. Under verifiable conditions on the model and performance measure, we establish strong consistency and a (martingale) central limit theorem for resulting performance estimates. We instantiate our framework with worked examples given stochastic or deterministic label oracle access. Both examples leverage Dirichlet-tree models for practical online evaluation, with the deterministic case achieving asymptotic optimality. Experiments on seven datasets demonstrate an average mean-squared error superior to state-of-the-art samplers on fixed label budgets.

This research proposes and evaluates scoring and assessment methods for Virtual Reality (VR) training simulators. VR simulators capture detailed n-dimensional human motion data which is useful for performance analysis. Custom made medical haptic VR training simulators were developed and used to record data from 271 trainees of multiple clinical experience levels. DTW Multivariate Prototyping (DTW-MP) is proposed. VR data was classified as Novice, Intermediate or Expert. Accuracy of algorithms applied for time-series classification were: dynamic time warping 1-nearest neighbor (DTW-1NN) 60%, nearest centroid SoftDTW classification 77.5%, Deep Learning: ResNet 85%, FCN 75%, CNN 72.5% and MCDCNN 28.5%. Expert VR data recordings can be used for guidance of novices. Assessment feedback can help trainees to improve skills and consistency. Motion analysis can identify different techniques used by individuals. Mistakes can be detected dynamically in real-time, raising alarms to prevent injuries.

Clustering is a ubiquitous task in data science. Compared to the commonly used $k$-means clustering algorithm, $k$-medoids clustering algorithms require the cluster centers to be actual data points and support arbitrary distance metrics, allowing for greater interpretability and the clustering of structured objects. Current state-of-the-art $k$-medoids clustering algorithms, such as Partitioning Around Medoids (PAM), are iterative and are quadratic in the dataset size $n$ for each iteration, being prohibitively expensive for large datasets. We propose Bandit-PAM, a randomized algorithm inspired by techniques from multi-armed bandits, that significantly improves the computational efficiency of PAM. We theoretically prove that Bandit-PAM reduces the complexity of each PAM iteration from $O(n^2)$ to $O(n \log n)$ and returns the same results with high probability, under assumptions on the data that often hold in practice. We empirically validate our results on several large-scale real-world datasets, including a coding exercise submissions dataset from Code.org, the 10x Genomics 68k PBMC single-cell RNA sequencing dataset, and the MNIST handwritten digits dataset. We observe that Bandit-PAM returns the same results as PAM while performing up to 200x fewer distance computations. The improvements demonstrated by Bandit-PAM enable $k$-medoids clustering on a wide range of applications, including identifying cell types in large-scale single-cell data and providing scalable feedback for students learning computer science online. We also release Python and C++ implementations of our algorithm.