相关论文: Tight lower bounds for Dynamic Time Warping

Computing an accurate mean of a set of time series is a critical task in applications like nearest-neighbor classification and clustering of time series. While there are many distance functions for time series, the most popular distance…

Distance weighted discrimination (DWD) is a margin-based classifier with an interesting geometric motivation. DWD was originally proposed as a superior alternative to the support vector machine (SVM), however DWD is yet to be popular…

In this paper, we study the design and analysis of a class of efficient algorithms for computing the Gromov-Wasserstein (GW) distance tailored to large-scale graph learning tasks. Armed with the Luo-Tseng error bound…

Weighted minwise hashing is a standard dimensionality reduction technique with applications to similarity search and large-scale kernel machines. We introduce a simple algorithm that takes a weighted set $x \in \mathbb{R}_{\geq 0}^{d}$ and…

Sliding-window aggregation is a widely-used approach for extracting insights from the most recent portion of a data stream. The aggregations of interest can usually be expressed as binary operators that are associative but not necessarily…

The project aims to research on combining deep learning specifically Long-Short Memory (LSTM) and basic statistics in multiple multistep time series prediction. LSTM can dive into all the pages and learn the general trends of variation in a…

We provide theoretical and empirical evidence that using tighter evidence lower bounds (ELBOs) can be detrimental to the process of learning an inference network by reducing the signal-to-noise ratio of the gradient estimator. Our results…

A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…

Dynamic Treatment Regimes (DTRs) provide a systematic framework for optimizing sequential decision-making in chronic disease management, where therapies must adapt to patients' evolving clinical profiles. Inverse probability weighting (IPW)…

Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, flow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system's description online as time…

Error bound condition has recently gained revived interest in optimization. It has been leveraged to derive faster convergence for many popular algorithms, including subgradient methods, proximal gradient method and accelerated proximal…

The expressivity of neural networks as a function of their depth, width and type of activation units has been an important question in deep learning theory. Recently, depth separation results for ReLU networks were obtained via a new…

Classic similarity measures of strings are longest common subsequence and Levenshtein distance (i.e., the classic edit distance). A classic similarity measure of curves is dynamic time warping. These measures can be computed by simple…

In this paper we tackle the problem of efficient video event detection. We argue that linear detection functions should be preferred in this regard due to their scalability and efficiency during estimation and evaluation. A popular approach…

Temporal difference (TD) learning is a foundational algorithm in reinforcement learning (RL). For nearly forty years, TD learning has served as a workhorse for applied RL as well as a building block for more complex and specialized…

As deep learning methods increasingly utilize sensitive data on a widespread scale, differential privacy (DP) offers formal guarantees to protect against information leakage during model training. A significant challenge remains in…

The short-time Fourier transform (STFT), or the discrete Gabor transform (DGT), has been extensively used in signal analysis and processing. Their properties are characterized by a window function. For signal processing, designing a special…

Reconstruction of a dynamical system from a time series requires the selection of two parameters, the embedding dimension $d_e$ and the embedding lag $\tau$. Many competing criteria to select these parameters exist, and all are heuristic.…

Contextual dueling bandits form a cornerstone of preference-based decision-making, with critical applications in recommender systems and large language model alignment. However, standard algorithms rely on the idealized assumption of…

[See the paper for the full abstract.] We show tight upper and lower bounds for time-space trade-offs for the $c$-Approximate Near Neighbor Search problem. For the $d$-dimensional Euclidean space and $n$-point datasets, we develop a data…