Compared to (simple) clustering data into K clusters, hierarchical clustering is much more complex and much less understood. One of the few seminal advances in hierarchical clusterings is the introduction by Dasgupta (2016) of a general yet simple paradigm of hierarchical clustering as loss minimization. This paradigm was expanded by Charikar and Chatziafratis (2016) and Roy and Pokutta (2016). The latter work also introduces a new set of techniques for obtaining hierarchical clusterings by showing that optimizing the loss can be relaxed to a Linear Program (LP). This paper introduces the first method to obtain optimality guarantees in the context of hierarchical clustering. Specifically, it is shown that the Sublevel Set (SS) paradigm invented by Meila (2018) for simple, nonhiearchical clustering, can be extended as well to hierarchical clustering. The main contribution is show that there is a natural distance between hierarchical clusterings whose properties can be exploited in the setting of the SS problem we will present in Section 3. The Sublevel Set method produces stability theorems of the following form.

We propose a novel \textit{online regularization} scheme for revenue-maximization in high-dimensional dynamic pricing algorithms. The online regularization scheme equips the proposed optimistic online regularized maximum likelihood pricing (\texttt{OORMLP}) algorithm with three major advantages: encode market noise knowledge into pricing process optimism; empower online statistical learning with always-validity over all decision points; envelop prediction error process with time-uniform non-asymptotic oracle inequalities. This type of non-asymptotic inference results allows us to design safer and more robust dynamic pricing algorithms in practice. In theory, the proposed \texttt{OORMLP} algorithm exploits the sparsity structure of high-dimensional models and obtains a logarithmic regret in a decision horizon. These theoretical advances are made possible by proposing an optimistic online LASSO procedure that resolves dynamic pricing problems at the \textit{process} level, based on a novel use of non-asymptotic martingale concentration. In experiments, we evaluate \texttt{OORMLP} in different synthetic pricing problem settings and observe that \texttt{OORMLP} performs better than \texttt{RMLP} proposed in \cite{javanmard2019dynamic}.

Recently, non-Euclidean spaces became popular for embedding structured data. Following hyperbolic and spherical spaces, more general product spaces have been proposed. However, searching for the best configuration of a product space is a resource-intensive procedure, which reduces the practical applicability of the idea. We introduce a novel concept of overlaying spaces that does not have the problem of configuration search and outperforms the competitors in structured data embedding tasks, when the aim is to preserve all distances. On the other hand, for local loss functions (e.g., for ranking losses), the dot-product similarity, which is often overlooked in graph embedding literature since it cannot be converted to a metric, outperforms all metric spaces. We discuss advantages of the dot product over proper metric spaces.

In recent years, machine learning algorithms, and more specially, deep learning algorithms, have been widely used in many fields, including cyber security. However, machine learning systems are vulnerable to adversarial attacks, and this limits the application of machine learning, especially in non-stationary, adversarial environments, such as the cyber security domain, where actual adversaries (e.g., malware developers) exist. This paper comprehensively summarizes the latest research on adversarial attacks against security solutions that are based on machine learning techniques and presents the risks they pose to cyber security solutions. First, we discuss the unique challenges of implementing end-to-end adversarial attacks in the cyber security domain. Following that, we define a unified taxonomy, where the adversarial attack methods are characterized based on their stage of occurrence, and the attacker's goals and capabilities. Then, we categorize the applications of adversarial attack techniques in the cyber security domain. Finally, we use our taxonomy to shed light on gaps in the cyber security domain that have already been addressed in other adversarial learning domains and discuss their impact on future adversarial learning trends in the cyber security domain.

We study the problem of estimating the parameters of a Boolean product distribution in $d$ dimensions, when the samples are truncated by a set $S \subset \{0, 1\}^d$ accessible through a membership oracle. This is the first time that the computational and statistical complexity of learning from truncated samples is considered in a discrete setting. We introduce a natural notion of fatness of the truncation set $S$, under which truncated samples reveal enough information about the true distribution. We show that if the truncation set is sufficiently fat, samples from the true distribution can be generated from truncated samples. A stunning consequence is that virtually any statistical task (e.g., learning in total variation distance, parameter estimation, uniformity or identity testing) that can be performed efficiently for Boolean product distributions, can also be performed from truncated samples, with a small increase in sample complexity. We generalize our approach to ranking distributions over $d$ alternatives, where we show how fatness implies efficient parameter estimation of Mallows models from truncated samples. Exploring the limits of learning discrete models from truncated samples, we identify three natural conditions that are necessary for efficient identifiability: (i) the truncation set $S$ should be rich enough; (ii) $S$ should be accessible through membership queries; and (iii) the truncation by $S$ should leave enough randomness in all directions. By carefully adapting the Stochastic Gradient Descent approach of (Daskalakis et al., FOCS 2018), we show that these conditions are also sufficient for efficient learning of truncated Boolean product distributions.

This paper studies few-shot relation extraction, which aims at predicting the relation for a pair of entities in a sentence by training with a few labeled examples in each relation. To more effectively generalize to new relations, in this paper we study the relationships between different relations and propose to leverage a global relation graph. We propose a novel Bayesian meta-learning approach to effectively learn the posterior distribution of the prototype vectors of relations, where the initial prior of the prototype vectors is parameterized with a graph neural network on the global relation graph. Moreover, to effectively optimize the posterior distribution of the prototype vectors, we propose to use the stochastic gradient Langevin dynamics, which is related to the MAML algorithm but is able to handle the uncertainty of the prototype vectors. The whole framework can be effectively and efficiently optimized in an end-to-end fashion. Experiments on two benchmark datasets prove the effectiveness of our proposed approach against competitive baselines in both the few-shot and zero-shot settings.

Feature selection is a core area of data mining with a recent innovation of graph-driven unsupervised feature selection for linked data. In this setting we have a dataset $\mathbf{Y}$ consisting of $n$ instances each with $m$ features and a corresponding $n$ node graph (whose adjacency matrix is $\mathbf{A}$) with an edge indicating that the two instances are similar. Existing efforts for unsupervised feature selection on attributed networks have explored either directly regenerating the links by solving for $f$ such that $f(\mathbf{y}_i,\mathbf{y}_j) \approx \mathbf{A}_{i,j}$ or finding community structure in $\mathbf{A}$ and using the features in $\mathbf{Y}$ to predict these communities. However, graph-driven unsupervised feature selection remains an understudied area with respect to exploring more complex guidance. Here we take the novel approach of first building a block model on the graph and then using the block model for feature selection. That is, we discover $\mathbf{F}\mathbf{M}\mathbf{F}^T \approx \mathbf{A}$ and then find a subset of features $\mathcal{S}$ that induces another graph to preserve both $\mathbf{F}$ and $\mathbf{M}$. We call our approach Block Model Guided Unsupervised Feature Selection (BMGUFS). Experimental results show that our method outperforms the state of the art on several real-world public datasets in finding high-quality features for clustering.

Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical properties in modern regimes where both the number of measurements and the number of unknown parameters is large is only recently emerging. In this paper, we characterize for the first time the fundamental limits on the statistical accuracy of convex ERM for inference in high-dimensional generalized linear models. For a stylized setting with Gaussian features and problem dimensions that grow large at a proportional rate, we start with sharp performance characterizations and then derive tight lower bounds on the estimation and prediction error that hold over a wide class of loss functions and for any value of the regularization parameter. Our precise analysis has several attributes. First, it leads to a recipe for optimally tuning the loss function and the regularization parameter. Second, it allows to precisely quantify the sub-optimality of popular heuristic choices: for instance, we show that optimally-tuned least-squares is (perhaps surprisingly) approximately optimal for standard logistic data, but the sub-optimality gap grows drastically as the signal strength increases. Third, we use the bounds to precisely assess the merits of ridge-regularization as a function of the over-parameterization ratio. Notably, our bounds are expressed in terms of the Fisher Information of random variables that are simple functions of the data distribution, thus making ties to corresponding bounds in classical statistics.

Establishing the precise timeline of a crime can be challenging as current analytical techniques used suffer from many limitations and are destructive to the body fluids encountered at crime scenes. Raman spectroscopy has demonstrated excellent potential in forensic science as it provides direct information about the structural and molecular changes without the need for processing or extracting samples. However, its current applicability is limited to pure body fluids, as signals from the substrate underlying these fluids greatly influence the current models used for age estimation. In this study, we utilized Raman spectroscopy to identify selective spectral markers that delineate the bloodstain age in the presence of interfering signals from the substrate. The pure bloodstains and the bloodstains on the substrate were aged for two weeks at 21 2 in the dark.

Want to be a part of an elite team where our innovative technical solutions are delivered to customers that advance the state of the art while addressing long-term problems of importance to national security? At our Leidos' Multi-Spectrum Warfare Research and Analytics Systems (MSWRAS) Division, an organization in the Leidos Innovation Center (LInC), we are looking for you, our next Scientist who specializes in remote sensing data analytics. Join our team of Ph.D. level peers in designing and developing advanced technology-based solutions for contract research and development projects working in our Arlington, VA office. Fun roles you will have in this job: Describe instances of successful, proven, and demonstrable experience contributing to the technical work as part of cross-discipline teams in the development and integration of software-based solutions for competitive, contract-based applied research programs Work with teams composed of members from industry, small businesses, and academic-based researchers and should have experience working on projects focused on multiple technical fields such as machine learning, artificial intelligence, engineering, and software development and integration Describe how the work products to which they contributed had solved customers' problems in such domains as energy, health, and national security or in the commercial sector Work within the MSWRAS Division and across the LInC, performing basic and applied contract research and development projects both leading and working under the guidance of senior scientists and engineers. Processing, interpreting and analyzing large volumes of data collected by remote sensing platforms but may also include other types of phenomenological data such as field measurements, or weather data Independently design and undertake new research as well as partner in a team environment across organizations Contribute to the development of creative and innovative R&D approaches to solving major remote sensing analytics challenges and work with potential sponsors (customers or internal champions) to secure funding for new research efforts based on those topics Contribute to the productivity of teams composed of fellow researchers, data scientists, data engineers, and software engineers to execute complex R&D programs Under the guidance of a senior scientist or engineer, design and develop or integrate secure and scalable applications that are part of broader solutions, that are applicable across multiple domains.