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This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
The success of deep neural networks hinges on our ability to accurately and efficiently optimize high-dimensional, non-convex functions. In this paper, we empirically investigate the loss functions of state-of-the-art networks, and how…
The top-k error is a common measure of performance in machine learning and computer vision. In practice, top-k classification is typically performed with deep neural networks trained with the cross-entropy loss. Theoretical results indeed…
This paper presents a method for robust optimization for online incremental Simultaneous Localization and Mapping (SLAM). Due to the NP-Hardness of data association in the presence of perceptual aliasing, tractable (approximate) approaches…
We study the following basic machine learning task: Given a fixed set of $d$-dimensional input points for a linear regression problem, we wish to predict a hidden response value for each of the points. We can only afford to attain the…
The lasso has become an important practical tool for high dimensional regression as well as the object of intense theoretical investigation. But despite the availability of efficient algorithms, the lasso remains computationally demanding…
This paper concerns the central issues of model robustness and sample efficiency in offline reinforcement learning (RL), which aims to learn to perform decision making from history data without active exploration. Due to uncertainties and…
In this work, to facilitate the real-time processing of multi-scan registration error minimization on factor graphs, we devise a point cloud downsampling algorithm based on coreset extraction. This algorithm extracts a subset of the…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
Simultaneous Localization and Mapping (SLAM) is considered an ever-evolving problem due to its usage in many applications. Evaluation of SLAM is done typically using publicly available datasets which are increasing in number and the level…
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…
This paper investigates the impact of the loss function in value-based methods for reinforcement learning through an analysis of underlying prediction objectives. We theoretically show that mean absolute error is a better prediction…
Dimension reduction is widely regarded as an effective way for decreasing the computation, storage and communication loads of data-driven intelligent systems, leading to a growing demand for statistical methods that allow analysis (e.g.,…
We solve a weakly supervised regression problem. Under "weakly" we understand that for some training points the labels are known, for some unknown, and for others uncertain due to the presence of random noise or other reasons such as lack…
We study the problem of robust time series analysis under the standard auto-regressive (AR) time series model in the presence of arbitrary outliers. We devise an efficient hard thresholding based algorithm which can obtain a consistent…
This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this…
Rough set is one of the important methods for rule acquisition and attribute reduction. The current goal of rough set attribute reduction focuses more on minimizing the number of reduced attributes, but ignores the spatial similarity…
Depth estimation from 2D images is a common computer vision task that has applications in many fields including autonomous vehicles, scene understanding and robotics. The accuracy of a supervised depth estimation method mainly relies on the…
This work constructs Jonson-Lindenstrauss embeddings with best accuracy, as measured by variance, mean-squared error and exponential concentration of the length distortion. Lower bounds for any data and embedding dimensions are determined,…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…