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This study investigates privacy leakage in dimensionality reduction methods through a novel machine learning-based reconstruction attack. Employing an \emph{informed adversary} threat model, we develop a neural network capable of reconstructing high-dimensional data from low-dimensional embeddings. We evaluate six popular dimensionality reduction techniques: PCA, sparse random projection (SRP), multidimensional scaling (MDS), Isomap, $t$-SNE, and UMAP. Using both MNIST and NIH Chest X-ray datasets, we perform a qualitative analysis to identify key factors affecting reconstruction quality. Furthermore, we assess the effectiveness of an additive noise mechanism in mitigating these reconstruction attacks.

We develop a statistical inference method for an optimal transport map between distributions on real numbers with uniform confidence bands. The concept of optimal transport (OT) is used to measure distances between distributions, and OT maps are used to construct the distance. OT has been applied in many fields in recent years, and its statistical properties have attracted much interest. In particular, since the OT map is a function, a uniform norm-based statistical inference is significant for visualization and interpretation. In this study, we derive a limit distribution of a uniform norm of an estimation error for the OT map, and then develop a uniform confidence band based on it. In addition to our limit theorem, we develop a bootstrap method with kernel smoothing, then also derive its validation and guarantee on an asymptotic coverage probability of the confidence band. Our proof is based on the functional delta method and the representation of OT maps on the reals., Comment: 37 pages

Labeling a large number of electronic health records is expensive and time consuming, and having a labeling assistant tool can significantly reduce medical experts' workload. Nevertheless, to gain the experts' trust, the tool must be able to explain the reasons behind its outputs. Motivated by this, we introduce Explainable Labeling Assistant (XLabel) a new visual-interactive tool for data labeling. At a high level, XLabel uses Explainable Boosting Machine (EBM) to classify the labels of each data point and visualizes heatmaps of EBM's explanations. As a case study, we use XLabel to help medical experts label electronic health records with four common non-communicable diseases (NCDs). Our experiments show that 1) XLabel helps reduce the number of labeling actions, 2) EBM as an explainable classifier is as accurate as other well-known machine learning models outperforms a rule-based model used by NCD experts, and 3) even when more than 40% of the records were intentionally mislabeled, EBM could recall the correct labels of more than 90% of these records., Comment: The detailed code, documentation and installation instructions of XLabel have been made available at https://github.com/donlapark/XLabel

Anomaly detection has emerged as a popular technique for detecting malicious activities in local area networks (LANs). Various aspects of LAN anomaly detection have been widely studied. Nonetheless, the privacy concern about individual users or their relationship in LAN has not been thoroughly explored in the prior work. In some realistic cases, the anomaly detection analysis needs to be carried out by an external party, located outside the LAN. Thus, it is important for the LAN admin to release LAN data to this party in a private way in order to protect privacy of LAN users; at the same time, the released data must also preserve the utility of being able to detect anomalies. This paper investigates the possibility of privately releasing ARP data that can later be used to identify anomalies in LAN. We present four approaches and show that they satisfy different levels of differential privacy - a rigorous and provable notion for quantifying privacy loss in a system. Our real-world experimental results confirm practical feasibility of our approaches. With a proper privacy budget, all of our approaches preserve more than 75% utility of detecting anomalies in the released data.

Given an empirical distribution $f(x)$ of sensitive data $x$, we consider the task of minimizing $F(y) = D_{\text{KL}} (f(x)\Vert y)$ over a probability simplex, while protecting the privacy of $x$. We observe that, if we take the exponential mechanism and use the KL divergence as the loss function, then the resulting algorithm is the Dirichlet mechanism that outputs a single draw from a Dirichlet distribution. Motivated by this, we propose a R\'enyi differentially private (RDP) algorithm that employs the Dirichlet mechanism to solve the KL divergence minimization task. In addition, given $f(x)$ as above and $\hat{y}$ an output of the Dirichlet mechanism, we prove a probability tail bound on $D_{\text{KL}} (f(x)\Vert \hat{y})$, which is then used to derive a lower bound for the sample complexity of our RDP algorithm. Experiments on real-world datasets demonstrate advantages of our algorithm over Gaussian and Laplace mechanisms in supervised classification and maximum likelihood estimation., Comment: 22 pages; 11 figures; code available at: https://github.com/donlapark/Dirichlet-Mechanism

Short-term precipitation forecasting is essential for planning of human activities in multiple scales, ranging from individuals' planning, urban management to flood prevention. Yet the short-term atmospheric dynamics are highly nonlinear that it cannot be easily captured with classical time series models. On the other hand, deep learning models are good at learning nonlinear interactions, but they are not designed to deal with the seasonality in time series. In this study, we aim to develop a forecasting model that can both handle the nonlinearities and detect the seasonality hidden within the daily precipitation data. To this end, we propose a seasonally-integrated autoencoder (SSAE) consisting of two long short-term memory (LSTM) autoencoders: one for learning short-term dynamics, and the other for learning the seasonality in the time series. Our experimental results show that not only does the SSAE outperform various time series models regardless of the climate type, but it also has low output variance compared to other deep learning models. The results also show that the seasonal component of the SSAE helped improve the correlation between the forecast and the actual values from 4% at horizon 1 to 37% at horizon 3., Comment: 35 pages, 13 figures

The Wasserstein distance provides a notion of dissimilarities between probability measures, which has recent applications in learning of structured data with varying size such as images and text documents. In this work, we study the $k$-nearest neighbor classifier ($k$-NN) of probability measures under the Wasserstein distance. We show that the $k$-NN classifier is not universally consistent on the space of measures supported in $(0,1)$. As any Euclidean ball contains a copy of $(0,1)$, one should not expect to obtain universal consistency without some restriction on the base metric space, or the Wasserstein space itself. To this end, via the notion of $\sigma$-finite metric dimension, we show that the $k$-NN classifier is universally consistent on spaces of measures supported in a $\sigma$-uniformly discrete set. In addition, by studying the geodesic structures of the Wasserstein spaces for $p=1$ and $p=2$, we show that the $k$-NN classifier is universally consistent on the space of measures supported on a finite set, the space of Gaussian measures, and the space of measures with densities expressed as finite wavelet series., Comment: Reorder contents by importance