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Daniel P. Palomar

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4 papers

2 author rows

NeurIPS Conference 2024 Conference Paper

Adaptive Passive-Aggressive Framework for Online Regression with Side Information

Runhao Shi
Jiaxi Ying
Daniel P. Palomar

The Passive-Aggressive (PA) method is widely used in online regression problems for handling large-scale streaming data, typically updating model parameters in a passive-aggressive manner based on whether the error exceeds a predefined threshold. However, this approach struggles with determining optimal thresholds and adapting to complex scenarios with side information, where tracking accuracy is not the sole metric in the regression model. To address these challenges, we introduce a novel adaptive framework that allows finer adjustments to the weight vector in PA using side information. This framework adaptively selects the threshold parameter in PA, theoretically ensuring convergence to the optimal setting. Additionally, we present an efficient implementation of our algorithm that significantly reduces computational complexity. Numerical experiments show that our model achieves outstanding performance associated with the side information while maintaining low tracking error, demonstrating marked improvements over traditional PA methods across various scenarios.

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ICML Conference 2023 Conference Paper

Adaptive Estimation of Graphical Models under Total Positivity

Jiaxi Ying
José Vinícius de Miranda Cardoso
Daniel P. Palomar

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. Such models have shown interesting properties, e. g. , the maximum likelihood estimator exists with as little as two observations in the case of M-matrices, and exists even with one observation in the case of diagonally dominant M-matrices. We propose an adaptive multiple-stage estimation method, which refines the estimate by solving a weighted $\ell_1$-regularized problem in each stage. We further design a unified framework based on gradient projection method to solve the regularized problem, equipped with different projections to handle the constraints of M-matrices and diagonally dominant M-matrices. Theoretical analysis of the estimation error is established. The proposed method outperforms state-of-the-art methods in estimating precision matrices and identifying graph edges, as evidenced by synthetic and financial time-series data sets.

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AAAI Conference 2022 Conference Paper

Efficient Algorithms for General Isotone Optimization

Xiwen Wang
Jiaxi Ying
José Vinícius de M. Cardoso
Daniel P. Palomar

Monotonicity is often a fundamental assumption involved in the modeling of a number of real-world applications. From an optimization perspective, monotonicity is formulated as partial order constraints among the optimization variables, commonly known as isotone optimization. In this paper, we develop an efficient, provable convergent algorithm for solving isotone optimization problems. The proposed algorithm is general in the sense that it can handle any arbitrary isotonic constraints and a wide range of objective functions. We evaluate our algorithm and state-of-the-art methods with experiments involving both synthetic and realworld data. The experimental results demonstrate that our algorithm is more efficient by one to four orders of magnitude than the state-of-the-art methods.

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JMLR Journal 2020 Journal Article

A Unified Framework for Structured Graph Learning via Spectral Constraints

Sandeep Kumar
Jiaxi Ying
José Vinícius de M. Cardoso
Daniel P. Palomar

Graph learning from data is a canonical problem that has received substantial attention in the literature. Learning a structured graph is essential for interpretability and identification of the relationships among data. In general, learning a graph with a specific structure is an NP-hard combinatorial problem and thus designing a general tractable algorithm is challenging. Some useful structured graphs include connected, sparse, multi-component, bipartite, and regular graphs. In this paper, we introduce a unified framework for structured graph learning that combines Gaussian graphical model and spectral graph theory. We propose to convert combinatorial structural constraints into spectral constraints on graph matrices and develop an optimization framework based on block majorization-minimization to solve structured graph learning problem. The proposed algorithms are provably convergent and practically amenable for a number of graph based applications such as data clustering. Extensive numerical experiments with both synthetic and real data sets illustrate the effectiveness of the proposed algorithms. An open source R package containing the code for all the experiments is available at https://CRAN.R-project.org/package=spectralGraphTopology. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2020. ( edit, beta )

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