Clustering is a widely used unsupervised learning method. The grouping is such that points in a cluster are similar to each other, and less similar to points in other clusters. Thus, it is up to the algorithm to find patterns in the data and group it for us and, depending on the algorithm used, we may end up with different clusters. There are 2 broad approaches for clustering: 1. Compactness -- Points that lie close to each other fall in the same cluster and are compact around the cluster center. The closeness can be measured by the distance between the observations.

This is an integrative review that address the question, "What makes for a good explanation?" with reference to AI systems. Pertinent literatures are vast. Thus, this review is necessarily selective. That said, most of the key concepts and issues are expressed in this Report. The Report encapsulates the history of computer science efforts to create systems that explain and instruct (intelligent tutoring systems and expert systems). The Report expresses the explainability issues and challenges in modern AI, and presents capsule views of the leading psychological theories of explanation. Certain articles stand out by virtue of their particular relevance to XAI, and their methods, results, and key points are highlighted. It is recommended that AI/XAI researchers be encouraged to include in their research reports fuller details on their empirical or experimental methods, in the fashion of experimental psychology research reports: details on Participants, Instructions, Procedures, Tasks, Dependent Variables (operational definitions of the measures and metrics), Independent Variables (conditions), and Control Conditions.

AI software is still software. Software engineers need better tools to make better use of AI software. For example, for software defect prediction and software text mining, the default tunings for software analytics tools can be improved with "hyperparameter optimization" tools that decide (e.g.,) how many trees are needed in a random forest. Hyperparameter optimization is unnecessarily slow when optimizers waste time exploring redundant options (i.e., pairs of tunings with indistinguishably different results). By ignoring redundant tunings, the Dodge(E) hyperparameter optimization tool can run orders of magnitude faster, yet still find better tunings than prior state-of-the-art algorithms (for software defect prediction and software text mining).

Spectral clustering algorithms typically require a priori selection of input parameters such as the number of clusters, a scaling parameter for the affinity measure, or ranges of these values for parameter tuning. Despite efforts for automating the process of spectral clustering, the task of grouping data in multi-scale and higher dimensional spaces is yet to be explored. This study presents a spectral clustering heuristic algorithm that obviates the need for an input by estimating the parameters from the data itself. Specifically, it introduces the heuristic of iterative eigengap search with (1) global scaling and (2) local scaling. These approaches estimate the scaling parameter and implement iterative eigengap quantification along a search tree to reveal dissimilarities at different scales of a feature space and identify clusters. The performance of these approaches has been tested on various real-world datasets of power variation with multi-scale nature and gene expression. Our findings show that iterative eigengap search with a PCA-based global scaling scheme can discover different patterns with an accuracy of higher than 90% in most cases without asking for a priori input information.

We focus on the commonly used synchronous Gradient Descent paradigm for large-scale distributed learning, for which there has been a growing interest to develop efficient and robust gradient aggregation strategies that overcome two key bottlenecks: communication bandwidth and stragglers' delays. In particular, Ring-AllReduce (RAR) design has been proposed to avoid bandwidth bottleneck at any particular node by allowing each worker to only communicate with its neighbors that are arranged in a logical ring. On the other hand, Gradient Coding (GC) has been recently proposed to mitigate stragglers in a master-worker topology by allowing carefully designed redundant allocation of the data set to the workers. We propose a joint communication topology design and data set allocation strategy, named CodedReduce (CR), that combines the best of both RAR and GC. That is, it parallelizes the communications over a tree topology leading to efficient bandwidth utilization, and carefully designs a redundant data set allocation and coding strategy at the nodes to make the proposed gradient aggregation scheme robust to stragglers. In particular, we quantify the communication parallelization gain and resiliency of the proposed CR scheme, and prove its optimality when the communication topology is a regular tree. Furthermore, we empirically evaluate the performance of our proposed CR design over Amazon EC2 and demonstrate that it achieves speedups of up to 18.9x and 7.9x, respectively over the benchmarks GC and RAR.

How can we learn to do probabilistic inference in a way that generalizes between models? Amortized variational inference learns for a single model, sharing statistical strength across observations. This benefits scalability and model learning, but does not help with generalization to new models. We propose meta-amortized variational inference, a framework that amortizes the cost of inference over a family of generative models. We apply this approach to deep generative models by introducing the MetaVAE: a variational autoencoder that learns to generalize to new distributions and rapidly solve new unsupervised learning problems using only a small number of target examples. Empirically, we validate the approach by showing that the MetaVAE can: (1) capture relevant sufficient statistics for inference, (2) learn useful representations of data for downstream tasks such as clustering, and (3) perform meta-density estimation on unseen synthetic distributions and out-of-sample Omniglot alphabets.

Erbium-doped fiber amplifier (EDFA) is an optical amplifier/repeater device used to boost the intensity of optical signals being carried through a fiber optic communication system. A highly accurate EDFA model is important because of its crucial role in optical network management and optimization. The input channels of an EDFA device are treated as either on or off, hence the input features are binary. Labeled training data is very expensive to collect for EDFA devices, therefore we devise an active learning strategy suitable for binary variables to overcome this issue. We propose to take advantage of sparse linear models to simplify the predictive model. This approach simultaneously improves prediction and accelerates active learning query generation. We show the performance of our proposed active learning strategies on simulated data and real EDFA data.

The (stochastic) gradient descent and the multiplicative update method are probably the most popular algorithms in machine learning. We introduce and study a new regularization which provides a unification of the additive and multiplicative updates. This regularization is derived from an hyperbolic analogue of the entropy function, which we call hypentropy. It is motivated by a natural extension of the multiplicative update to negative numbers. The hypentropy has a natural spectral counterpart which we use to derive a family of matrix-based updates that bridge gradient methods and the multiplicative method for matrices. While the latter is only applicable to positive semi-definite matrices, the spectral hypentropy method can naturally be used with general rectangular matrices. We analyze the new family of updates by deriving tight regret bounds. We study empirically the applicability of the new update for settings such as multiclass learning, in which the parameters constitute a general rectangular matrix.

We explore and expand the $\textit{Soft Nearest Neighbor Loss}$ to measure the $\textit{entanglement}$ of class manifolds in representation space: i.e., how close pairs of points from the same class are relative to pairs of points from different classes. We demonstrate several use cases of the loss. As an analytical tool, it provides insights into the evolution of class similarity structures during learning. Surprisingly, we find that $\textit{maximizing}$ the entanglement of representations of different classes in the hidden layers is beneficial for discrimination in the final layer, possibly because it encourages representations to identify class-independent similarity structures. Maximizing the soft nearest neighbor loss in the hidden layers leads not only to improved generalization but also to better-calibrated estimates of uncertainty on outlier data. Data that is not from the training distribution can be recognized by observing that in the hidden layers, it has fewer than the normal number of neighbors from the predicted class.

Gibbs-ERM learning is a natural idealized model of learning with stochastic optimization algorithms (such as Stochastic Gradient Langevin Dynamics and ---to some extent--- Stochastic Gradient Descent), while it also arises in other contexts, including PAC-Bayesian theory, and sampling mechanisms. In this work we study the excess risk suffered by a Gibbs-ERM learner that uses non-convex, regularized empirical risk with the goal to understand the interplay between the data-generating distribution and learning in large hypothesis spaces. Our main results are distribution-dependent upper bounds on several notions of excess risk. We show that, in all cases, the distribution-dependent excess risk is essentially controlled by the effective dimension $\mathrm{tr}\left(\boldsymbol{H}^{\star} (\boldsymbol{H}^{\star} + \lambda \boldsymbol{I})^{-1}\right)$ of the problem, where $\boldsymbol{H}^{\star}$ is the Hessian matrix of the risk at a local minimum. This is a well-established notion of effective dimension appearing in several previous works, including the analyses of SGD and ridge regression, but ours is the first work that brings this dimension to the analysis of learning using Gibbs densities. The distribution-dependent view we advocate here improves upon earlier results of Raginsky et al. (2017), and can yield much tighter bounds depending on the interplay between the data-generating distribution and the loss function. The first part of our analysis focuses on the localized excess risk in the vicinity of a fixed local minimizer. This result is then extended to bounds on the global excess risk, by characterizing probabilities of local minima (and their complement) under Gibbs densities, a results which might be of independent interest.