Sliced Wasserstein (SW) distance suffers from redundant projections due to independent uniform random projecting directions. To partially overcome the issue, max K sliced Wasserstein (Max-K-SW) distance ($K\geq 1$), seeks the best discriminative orthogonal projecting directions. Despite being able to reduce the number of projections, the metricity of Max-K-SW cannot be guaranteed in practice due to the non-optimality of the optimization. Moreover, the orthogonality constraint is also computationally expensive and might not be effective. To address the problem, we introduce a new family of SW distances, named Markovian sliced Wasserstein (MSW) distance, which imposes a first-order Markov structure on projecting directions. We discuss various members of MSW by specifying the Markov structure including the prior distribution, the transition distribution, and the burning and thinning technique. Moreover, we investigate the theoretical properties of MSW including topological properties (metricity, weak convergence, and connection to other distances), statistical properties (sample complexity, and Monte Carlo estimation error), and computational properties (computational complexity and memory complexity). Finally, we compare MSW distances with previous SW variants in various applications such as gradient flows, color transfer, and deep generative modeling to demonstrate the favorable performance of MSW.

Simplicity bias is an intriguing phenomenon prevalent in various input-output maps, characterized by a preference for simpler, more regular, or symmetric outputs. Notably, these maps typically feature high-probability outputs with simple patterns, whereas complex patterns are exponentially less probable. This bias has been extensively examined and attributed to principles derived from algorithmic information theory and algorithmic probability. In a significant advancement, it has been demonstrated that the renowned logistic map $x_{k+1}=\mu x_k(1-x_k)$, and other one-dimensional maps exhibit simplicity bias when conceptualized as input-output systems. Building upon this foundational work, our research delves into the manifestations of simplicity bias within the random logistic map, specifically focusing on scenarios involving additive noise. This investigation is driven by the overarching goal of formulating a comprehensive theory for the prediction and analysis of time series.Our primary contributions are multifaceted. We discover that simplicity bias is observable in the random logistic map for specific ranges of $\mu$ and noise magnitudes. Additionally, we find that this bias persists even with the introduction of small measurement noise, though it diminishes as noise levels increase. Our studies also revisit the phenomenon of noise-induced chaos, particularly when $\mu=3.83$, revealing its characteristics through complexity-probability plots. Intriguingly, we employ the logistic map to underscore a paradoxical aspect of data analysis: more data adhering to a consistent trend can occasionally lead to reduced confidence in extrapolation predictions, challenging conventional wisdom.We propose that adopting a probability-complexity perspective in analyzing dynamical systems could significantly enrich statistical learning theories related to series prediction.

We study a principal component analysis problem under the spiked Wishart model in which the structure in the signal is captured by a class of union-of-subspace models. This general class includes vanilla sparse PCA as well as its variants with graph sparsity. With the goal of studying these problems under a unified statistical and computational lens, we establish fundamental limits that depend on the geometry of the problem instance, and show that a natural projected power method exhibits local convergence to the statistically near-optimal neighborhood of the solution. We complement these results with end-to-end analyses of two important special cases given by path and tree sparsity in a general basis, showing initialization methods and matching evidence of computational hardness. Overall, our results indicate that several of the phenomena observed for vanilla sparse PCA extend in a natural fashion to its structured counterparts.

This study developed a generative adversarial network (GAN)-based defense method for traffic sign classification in an autonomous vehicle (AV), referred to as the attack-resilient GAN (AR-GAN). The novelty of the AR-GAN lies in (i) assuming zero knowledge of adversarial attack models and samples and (ii) providing consistently high traffic sign classification performance under various adversarial attack types. The AR-GAN classification system consists of a generator that denoises an image by reconstruction, and a classifier that classifies the reconstructed image. The authors have tested the AR-GAN under no-attack and under various adversarial attacks, such as Fast Gradient Sign Method (FGSM), DeepFool, Carlini and Wagner (C&W), and Projected Gradient Descent (PGD). The authors considered two forms of these attacks, i.e., (i) black-box attacks (assuming the attackers possess no prior knowledge of the classifier), and (ii) white-box attacks (assuming the attackers possess full knowledge of the classifier). The classification performance of the AR-GAN was compared with several benchmark adversarial defense methods. The results showed that both the AR-GAN and the benchmark defense methods are resilient against black-box attacks and could achieve similar classification performance to that of the unperturbed images. However, for all the white-box attacks considered in this study, the AR-GAN method outperformed the benchmark defense methods. In addition, the AR-GAN was able to maintain its high classification performance under varied white-box adversarial perturbation magnitudes, whereas the performance of the other defense methods dropped abruptly at increased perturbation magnitudes.

This document presents a stock market analysis conducted on a dataset consisting of 750 instances and 16 attributes donated in 2014-10-23. The analysis includes an exploratory data analysis (EDA) section, feature engineering, data preparation, model selection, and insights from the analysis. The Fama French 3-factor model is also utilized in the analysis. The results of the analysis are presented, with linear regression being the best-performing model.

Semantic embeddings play a crucial role in natural language-based information retrieval. Embedding models represent words and contexts as vectors whose spatial configuration is derived from the distribution of words in large text corpora. While such representations are generally very powerful, they might fail to account for fine-grained domain-specific nuances. In this article, we investigate this uncertainty for the domain of characterizations of expressive piano performance. Using a music research dataset of free text performance characterizations and a follow-up study sorting the annotations into clusters, we derive a ground truth for a domain-specific semantic similarity structure. We test five embedding models and their similarity structure for correspondence with the ground truth. We further assess the effects of contextualizing prompts, hubness reduction, cross-modal similarity, and k-means clustering. The quality of embedding models shows great variability with respect to this task; more general models perform better than domain-adapted ones and the best model configurations reach human-level agreement.

Sperm whales (Physeter macrocephalus) navigate underwater with a series of impulsive, click-like sounds known as echolocation clicks. These clicks are characterized by a multipulse structure (MPS) that serves as a distinctive pattern. In this work, we use the stability of the MPS as a detection metric for recognizing and classifying the presence of clicks in noisy environments. To distinguish between noise transients and to handle simultaneous emissions from multiple sperm whales, our approach clusters a time series of MPS measures while removing potential clicks that do not fulfil the limits of inter-click interval, duration and spectrum. As a result, our approach can handle high noise transients and low signal-to-noise ratio. The performance of our detection approach is examined using three datasets: seven months of recordings from the Mediterranean Sea containing manually verified ambient noise; several days of manually labelled data collected from the Dominica Island containing approximately 40,000 clicks from multiple sperm whales; and a dataset from the Bahamas containing 1,203 labelled clicks from a single sperm whale. Comparing with the results of two benchmark detectors, a better trade-off between precision and recall is observed as well as a significant reduction in false detection rates, especially in noisy environments. To ensure reproducibility, we provide our database of labelled clicks along with our implementation code.

We study the sample complexity of sample average approximation (SAA) and its simple variations, referred to as the regularized SAA (RSAA), in solving convex and strongly convex stochastic programming (SP) problems under heavy-tailed-ness, non-Lipschitz-ness, and/or high dimensionality. The presence of such irregularities underscores critical vacua in the literature. In response, this paper presents three sets of results: First, we show that the (R)SAA is effective even if the objective function is not necessarily Lipschitz and the underlying distribution admits some bounded central moments only at (near-)optimal solutions. Second, when the SP's objective function is the sum of a smooth term and a Lipschitz term, we prove that the (R)SAA's sample complexity is completely independent from any complexity measures (e.g., the covering number) of the feasible region. Third, we explicate the (R)SAA's sample complexities with regard to the dependence on dimensionality $d$: When some $p$th ($p\geq 2$) central moment of the underlying distribution is bounded, we show that the required sample size grows at a rate no worse than $\mathcal O\left(p d^{2/p}\right)$ under any one of the three structural assumptions: (i) strong convexity w.r.t. the $q$-norm ($q\geq 1$); (ii) the combination of restricted strong convexity and sparsity; and (iii) a dimension-insensitive $q$-norm of an optimal solution. In both cases of (i) and (iii), it is further required that $p\leq q/(q-1)$. As a direct implication, the (R)SAA's complexity becomes (poly-)logarithmic in $d$, whenever $p\geq c\cdot \ln d$ is admissible for some constant $c>0$. These new results deviate from the SAA's typical sample complexities that grow polynomially with $d$. Part of our proof is based on the average-replace-one (RO) stability, which appears to be novel for the (R)SAA's analyses.

We consider the problem of tracking multiple, unknown, and time-varying numbers of objects using a distributed network of heterogeneous sensors. In an effort to derive a formulation for practical settings, we consider limited and unknown sensor field-of-views (FoVs), sensors with limited local computational resources and communication channel capacity. The resulting distributed multi-object tracking algorithm involves solving an NP-hard multidimensional assignment problem either optimally for small-size problems or sub-optimally for general practical problems. For general problems, we propose an efficient distributed multi-object tracking algorithm that performs track-to-track fusion using a clustering-based analysis of the state space transformed into a density space to mitigate the complexity of the assignment problem. The proposed algorithm can more efficiently group local track estimates for fusion than existing approaches. To ensure we achieve globally consistent identities for tracks across a network of nodes as objects move between FoVs, we develop a graph-based algorithm to achieve label consensus and minimise track segmentation. Numerical experiments with a synthetic and a real-world trajectory dataset demonstrate that our proposed method is significantly more computationally efficient than state-of-the-art solutions, achieving similar tracking accuracy and bandwidth requirements but with improved label consistency.

In the arena of privacy-preserving machine learning, differentially private stochastic gradient descent (DP-SGD) has outstripped the objective perturbation mechanism in popularity and interest. Though unrivaled in versatility, DP-SGD requires a non-trivial privacy overhead (for privately tuning the model's hyperparameters) and a computational complexity which might be extravagant for simple models such as linear and logistic regression. This paper revamps the objective perturbation mechanism with tighter privacy analyses and new computational tools that boost it to perform competitively with DP-SGD on unconstrained convex generalized linear problems.