284 research outputs found
Distribution-Free Model-Agnostic Regression Calibration via Nonparametric Methods
In this paper, we consider the uncertainty quantification problem for
regression models. Specifically, we consider an individual calibration
objective for characterizing the quantiles of the prediction model. While such
an objective is well-motivated from downstream tasks such as newsvendor cost,
the existing methods have been largely heuristic and lack of statistical
guarantee in terms of individual calibration. We show via simple examples that
the existing methods focusing on population-level calibration guarantees such
as average calibration or sharpness can lead to harmful and unexpected results.
We propose simple nonparametric calibration methods that are agnostic of the
underlying prediction model and enjoy both computational efficiency and
statistical consistency. Our approach enables a better understanding of the
possibility of individual calibration, and we establish matching upper and
lower bounds for the calibration error of our proposed methods. Technically,
our analysis combines the nonparametric analysis with a covering number
argument for parametric analysis, which advances the existing theoretical
analyses in the literature of nonparametric density estimation and quantile
bandit problems. Importantly, the nonparametric perspective sheds new
theoretical insights into regression calibration in terms of the curse of
dimensionality and reconciles the existing results on the impossibility of
individual calibration. To our knowledge, we make the first effort to reach
both individual calibration and finite-sample guarantee with minimal
assumptions in terms of conformal prediction. Numerical experiments show the
advantage of such a simple approach under various metrics, and also under
covariates shift. We hope our work provides a simple benchmark and a starting
point of theoretical ground for future research on regression calibration.Comment: Accepted at NeurIPS 2023 and update a camera-ready version; Add some
experiments and literature review
Predict-then-Calibrate: A New Perspective of Robust Contextual LP
Contextual optimization, also known as predict-then-optimize or prescriptive
analytics, considers an optimization problem with the presence of covariates
(context or side information). The goal is to learn a prediction model (from
the training data) that predicts the objective function from the covariates,
and then in the test phase, solve the optimization problem with the covariates
but without the observation of the objective function. In this paper, we
consider a risk-sensitive version of the problem and propose a generic
algorithm design paradigm called predict-then-calibrate. The idea is to first
develop a prediction model without concern for the downstream risk profile or
robustness guarantee, and then utilize calibration (or recalibration) methods
to quantify the uncertainty of the prediction. While the existing methods
suffer from either a restricted choice of the prediction model or strong
assumptions on the underlying data, we show the disentangling of the prediction
model and the calibration/uncertainty quantification has several advantages.
First, it imposes no restriction on the prediction model and thus fully
unleashes the potential of off-the-shelf machine learning methods. Second, the
derivation of the risk and robustness guarantee can be made independent of the
choice of the prediction model through a data-splitting idea. Third, our
paradigm of predict-then-calibrate applies to both (risk-sensitive) robust and
(risk-neutral) distributionally robust optimization (DRO) formulations.
Theoretically, it gives new generalization bounds for the contextual LP problem
and sheds light on the existing results of DRO for contextual LP. Numerical
experiments further reinforce the advantage of the predict-then-calibrate
paradigm in that an improvement on either the prediction model or the
calibration model will lead to a better final performance.Comment: 30 pages, 8 figure
Rhubarb alleviates hyperoxia induced lung injury in neonatal rats with bronchopulmonary dysplasia by inhibiting inflammation
Purpose: To investigate the effect of rhubarb on hyperoxia-induced lung injury in neonatal rats with bronchopulmonary dysplasia (BPD), and the underlying mechanism.Methods: Sixty 4-day-old neonatal rats were assigned to air control, BPD, and rhubarb intervention groups, with 20 rats in each group. Immunoblotting was employed to assay NF-κB expression. Levels of malondialdehyde (MDA) and SOD were determined spectrophotometrically, while ELISA was used to measure serum levels of IL-6, IL-8 and TNF-α.Results: The peripheral blood levels of TNF-α, IL-8 and IL-1β were markedly higher in BPD-exposed rats than in the air control rats, while peripheral blood levels of TNF-α, IL-8 and IL-1β were reduced in rhubarb intervention rats, relative to BPD-exposed rats. The activity of SOD was markedly lower in lung tissue of BPD rats than in lung tissue of air control rats, while MDA level was markedly elevated in BPD rats (p < 0.05). There was marked up-regulation of NF-κB p65 expression in BPD-exposed rats, relative to air control rats, but it was markedly lower in rhubarb intervention rats than in hyperoxia model rats (p< 0.05).Conclusion: Rhubarb mitigated hyperoxia-induced inflammation, oxidative stress and lung injury in BPD neonatal rat model by inhibiting oxidative stress and reducing the levels of inflammatory factors
Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming
In this paper, we study the predict-then-optimize problem where the output of
a machine learning prediction task is used as the input of some downstream
optimization problem, say, the objective coefficient vector of a linear
program. The problem is also known as predictive analytics or contextual linear
programming. The existing approaches largely suffer from either (i)
optimization intractability (a non-convex objective function)/statistical
inefficiency (a suboptimal generalization bound) or (ii) requiring strong
condition(s) such as no constraint or loss calibration. We develop a new
approach to the problem called \textit{maximum optimality margin} which designs
the machine learning loss function by the optimality condition of the
downstream optimization. The max-margin formulation enjoys both computational
efficiency and good theoretical properties for the learning procedure. More
importantly, our new approach only needs the observations of the optimal
solution in the training data rather than the objective function, which makes
it a new and natural approach to the inverse linear programming problem under
both contextual and context-free settings; we also analyze the proposed method
under both offline and online settings, and demonstrate its performance using
numerical experiments.Comment: to be published in ICML 202
Decomposed Soft Prompt Guided Fusion Enhancing for Compositional Zero-Shot Learning
Compositional Zero-Shot Learning (CZSL) aims to recognize novel concepts
formed by known states and objects during training. Existing methods either
learn the combined state-object representation, challenging the generalization
of unseen compositions, or design two classifiers to identify state and object
separately from image features, ignoring the intrinsic relationship between
them. To jointly eliminate the above issues and construct a more robust CZSL
system, we propose a novel framework termed Decomposed Fusion with Soft Prompt
(DFSP)1, by involving vision-language models (VLMs) for unseen composition
recognition. Specifically, DFSP constructs a vector combination of learnable
soft prompts with state and object to establish the joint representation of
them. In addition, a cross-modal decomposed fusion module is designed between
the language and image branches, which decomposes state and object among
language features instead of image features. Notably, being fused with the
decomposed features, the image features can be more expressive for learning the
relationship with states and objects, respectively, to improve the response of
unseen compositions in the pair space, hence narrowing the domain gap between
seen and unseen sets. Experimental results on three challenging benchmarks
demonstrate that our approach significantly outperforms other state-of-the-art
methods by large margins.Comment: 10 pages included reference, conferenc
Numerical study of stall inception in a transonic axial compressor rotor based on the throttle model
The goal of the current paper is to investigate inner flow behavior on stall inception in a transonic compressor rotor. The stall inception process is numerically carried out by unsteady 3-D simulations based on the throttle model. The current study shows that stall starts from the tip of the blade, and stall cell extends to the axial, circumferential and radial directions. Through the comparison of flow transition characteristics at different flow rate conditions, the interface between the incoming flow and tip clearance flow shifts forward to the upstream as the mass flow decreases. Eventually, the shock detaches from the blade leading edge, and tip clearance flow spills into the adjacent blade passage, thus stall happens in the affected blade passages
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