Sparse Modeling: Theory, Algorithms, and Applications (Hardcover)

Sparse models are particularly useful in scientific applications, such as biomarker discovery in genetic or neuroimaging data, where the interpretability of a predictive model is essential. Sparsity can also dramatically improve the cost efficiency of signal processing.

Sparse Modeling: Theory, Algorithms, and Applications provides an introduction to the growing field of sparse modeling, including application examples, problem formulations that yield sparse solutions, algorithms for finding such solutions, and recent theoretical results on sparse recovery. The book gets you up to speed on the latest sparsity-related developments and will motivate you to continue learning about the field.

The authors first present motivating examples and a high-level survey of key recent developments in sparse modeling. The book then describes optimization problems involving commonly used sparsity-enforcing tools, presents essential theoretical results, and discusses several state-of-the-art algorithms for finding sparse solutions.

The authors go on to address a variety of sparse recovery problems that extend the basic formulation to more sophisticated forms of structured sparsity and to different loss functions. They also examine a particular class of sparse graphical models and cover dictionary learning and sparse matrix factorizations.

稀疏模型在科學應用中特別有用，例如在基因或神經影像數據中進行生物標誌物發現，預測模型的可解釋性至關重要。稀疏性還可以大幅提高信號處理的成本效益。

《稀疏建模：理論、算法和應用》介紹了稀疏建模這一快速發展的領域，包括應用示例、產生稀疏解的問題形式、尋找這些解的算法以及關於稀疏恢復的最新理論結果。本書將使您了解最新的稀疏相關發展，並激勵您繼續學習這一領域。

作者首先提出了激勵性的例子和對稀疏建模的關鍵最新發展的高層次調查。然後，本書描述了涉及常用稀疏強制工具的優化問題，介紹了基本理論結果，並討論了幾種尋找稀疏解的最先進算法。

作者還討論了各種稀疏恢復問題，將基本形式擴展到更複雜的結構稀疏形式和不同的損失函數。他們還研究了一類特定的稀疏圖模型，並涵蓋了字典學習和稀疏矩陣分解。