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A pareto dominance principle for data-driven optimization
Get PDFWe propose a statistically optimal approach to construct data-driven decisions
for stochastic optimization problems. Fundamentally, a data-driven decision is simply a
function that maps the available training data to a feasible action. It can always be expressed
as the minimizer of a surrogate optimization model constructed from the data. The quality
of a data-driven decision is measured by its out-of-sample risk. An additional quality measure
is its out-of-sample disappointment, which we define as the probability that the out-of-
sample risk exceeds the optimal value of the surrogate optimization model. The crux of
data-driven optimization is that the data-generating probability measure is unknown. An
ideal data-driven decision should therefore minimize the out-of-sample risk simultaneously
with respect to every conceivable probability measure (and thus in particular with respect to
the unknown true measure). Unfortunately, such ideal data-driven decisions are generally
unavailable. This prompts us to seek data-driven decisions that minimize the in-sample risk
subject to an upper bound on the out-of-sample disappointment—again simultaneously
with respect to every conceivable probability measure. We prove that such Pareto dominant
data-driven decisions exist under conditions that allow for interesting applications: The
unknown data-generating probability measure must belong to a parametric ambiguity set,
and the corresponding parameters must admit a sufficient statistic that satisfies a large deviation
principle. If these conditions hold, we can further prove that the surrogate optimization
model generating the optimal data-driven decision must be a distributionally robust
optimization problem constructed from the sufficient statistic and the rate function of its
large deviation principle. This shows that the optimal method for mapping data to decisions
is, in a rigorous statistical sense, to solve a distributionally robust optimization model.
Maybe surprisingly, this result holds irrespective of whether the original stochastic optimization
problem is convex or not and holds even when the training data are not independent
and identically distributed. As a byproduct, our analysis reveals how the structural properties
of the data-generating stochastic process impact the shape of the ambiguity set underlying
the optimal distributionally robust optimization model
DPSNN: Spiking neural network for low-latency streaming speech enhancement
Get PDFSpeech enhancement improves communication in noisy environments, affecting areas such as automatic speech recognition (ASR), hearing aids, and telecommunications. With these domains typically being power-constrained and event-based, and often requiring low latency, neuromorphic algorithms–particularly spiking neural networks (SNNs)–hold significant potential. However, current effective SNN solutions require a long temporal window to calculate Short Time Fourier Transforms (STFTs) and thus impose substantial latency, typically around 32 ms, which is too long for applications such as hearing aids. Inspired by the Dual-Path Recurrent Neural Network (DPRNN) in deep neural networks (DNNs), we develop a two-phase time-domain streaming SNN fframework for speech enhancement, named Dual-Path Spiking Neural Network (DPSNN). DPSNNs achieve low latency by replacing the STFT and inverse STFT (iSTFT) in traditional frequency-domain models with a learned convolutional encoder and decoder. In the DPSNN, the first phase uses Spiking Convolutional Neural Networks (SCNNs) to capture temporal contextual information, while the second phase uses Spiking Recurrent Neural Networks (SRNNs) to focus on frequency-related features. In addition, threshold-based activation suppression, along with L1 regularization loss, is applied to specific non-spiking layers in DPSNNs to further improve their energy efficiency. Evaluating on the Voice Cloning Toolkit (VCTK) Corpus and Intel N-DNS Challenge dataset, our approach demonstrates excellent performance in speech objective metrics, along with the very low latency (approximately 5 ms) required for applications like hearing aids
