A Smooth Primal-Dual Optimization Framework for Nonsmooth Composite Convex Minimization

Tran-Dinh, Quoc; Fercoq, Olivier; Cevher, Volkan

doi:10.1137/16m1093094

Cited by 58 publications

(119 citation statements)

References 70 publications

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“…Indeed, solving a single optimization problem with the HGL norm, using DecOpt [12], requires on average approximately 0.1 s, while the linear decoder requires only approximately 10 −5 s for a signal with 256 samples.…”

Section: Numerical Resultsmentioning

confidence: 99%

DCT Learning-Based Hardware Design for Neural Signal Acquisition Systems

Aprile

Wüthrich

Baldassarre³

et al. 2017

Proceedings of the Computing Frontiers Conference

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This work presents an area and power efficient encoding system for wireless implantable devices capable of monitoring the electrical activity of the brain. Such devices are becoming an important tool for understanding, real-time monitoring, and potentially treating mental diseases such as epilepsy and depression. Recent advances on compressive sensing (CS) have shown a huge potential for sub-Nyquist sampling of neuronal signals. However, its implementation is still facing critical issues in delivering sufficient performance and in hardware complexity. In this work, we explore the tradeoffs between area and power requirements applying a novel DCT Learning-Based Compressive Subsampling approach on a human iEEG dataset. The proposed method achieves compression rates up to 64×, increasing the reconstruction performance and reducing the wireless transmission costs with respect to recent state-of-art. This new fully digital architecture handles the data compression of each individual neural acquisition channel with an area of 490 × 650µm in 0.18 µm CMOS technology, and a power dissipation of only 2µW .

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Section: Numerical Resultsmentioning

confidence: 99%

DCT Learning-Based Hardware Design for Neural Signal Acquisition Systems

Aprile

Wüthrich

Baldassarre³

et al. 2017

Proceedings of the Computing Frontiers Conference

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“…In such a situation, efficient alternatives are primal-dual methods. Various references on these methods include [46][47][48] and references therein. These methods are basically built based on representing h via its Fenchel conjugate function h * , defined as The duality theory shows the existence of a dual problem to a given primal problem [43,Chapter 19] and puts them together.…”

Section: A Primal-dual First-order Methodsmentioning

confidence: 99%

“…In such a situation, efficient alternatives are primal‐dual methods. Various references on these methods include and references therein. These methods are basically built based on representing h via its Fenchel conjugate function h * , defined as

h^{*} ((), d) = \sup_{boldc \in ℝ^{n}} c^{⊤} boldd - h ((), c) .

…”

Section: Convex Optimization Of Energies Regressionmentioning

confidence: 99%

Chemical machine learning with kernels: The impact of loss functions

Nguyen

Lin

et al. 2019

Int J of Quantum Chemistry

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Machine learning promises to accelerate materials discovery by allowing computational efficient property predictions from a small number of reference calculations. As a result, the literature has spent a considerable effort in designing representations that capture basic physical properties. Our work focuses on the less‐studied learning formulations in this context in order to exploit inner structures in the prediction errors. In particular, we propose to directly optimize basic loss functions of the prediction error metrics typically used in the literature, such as the mean absolute error or the worst case error. In some instances, a proper choice of the loss function can directly reduce reasonably the prediction performance in the desired metric, albeit at the cost of additional computations during training. To support this claim, we describe the statistical learning theoretic foundations, and provide supporting numerical evidence with the prediction of atomization energies for a database of small organic molecules.

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“…In summary, for this data set, replacing the random index set coming from the randomized approach with the learned indices leads to a noticeable improvement, whereas the improvements from switching to non-linear decoders are marginal. It should be noted that these decoders incur heavy computational costs; some running times are summarized in Table I based on a state-of-the-art primal-dual decomposition method [26]. As the Kenya data set size is quite limited, we performed similar experiments on a much larger data set called ImageNet.…”

Section: A Kenya and Imagenet Data Setsmentioning

confidence: 99%

Learning-Based Compressive Subsampling

Baldassarre

Scarlett

et al. 2016

IEEE J. Sel. Top. Signal Process.

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The problem of recovering a structured signal x ∈ C p from a set of dimensionality-reduced linear measurements b = Ax arises in a variety of applications, such as medical imaging, spectroscopy, Fourier optics, and computerized tomography. Due to computational and storage complexity or physical constraints imposed by the problem, the measurement matrix A ∈ C n×p is often of the form A = PΩΨ for some orthonormal basis matrix Ψ ∈ C p×p and subsampling operator PΩ : C p → C n that selects the rows indexed by Ω. This raises the fundamental question of how best to choose the index set Ω in order to optimize the recovery performance. Previous approaches to addressing this question rely on non-uniform random subsampling using application-specific knowledge of the structure of x. In this paper, we instead take a principled learning-based approach in which a fixed index set is chosen based on a set of training signals x1, . . . , xm. We formulate combinatorial optimization problems seeking to maximize the energy captured in these signals in an average-case or worst-case sense, and we show that these can be efficiently solved either exactly or approximately via the identification of modularity and submodularity structures. We provide both deterministic and statistical theoretical guarantees showing how the resulting measurement matrices perform on signals differing from the training signals, and we provide numerical examples showing our approach to be effective on a variety of data sets.

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A Smooth Primal-Dual Optimization Framework for Nonsmooth Composite Convex Minimization

Cited by 58 publications

References 70 publications

DCT Learning-Based Hardware Design for Neural Signal Acquisition Systems

DCT Learning-Based Hardware Design for Neural Signal Acquisition Systems

Chemical machine learning with kernels: The impact of loss functions

Learning-Based Compressive Subsampling

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