Ensuring that the outputs of neural networks satisfy specific constraints is crucial for applying neural networks to real-life decision-making problems. In this paper, we consider making a batch of neural network outputs satisfy bounded and general linear constraints.

Diffusion planning has been recognized as an effective decision-making paradigm in various domains. The capability of generating high-quality long-horizon trajectories makes it a promising research direction. However, existing diffusion planning methods suffer from low decision-making frequencies due to the expensive iterative sampling cost.

Learning with rejection is an important framework that can refrain from making predictions to avoid critical mispredictions by balancing between prediction and rejection. Previous studies on cost-based rejection only focused on the classification setting, which cannot handle the continuous and infinite target space in the regression setting. In this paper, we investigate a novel regression problem called regression with cost-based rejection, where the model can reject to make predictions on some examples given certain rejection costs. To solve this problem, we first formulate the expected risk for this problem and then derive the Bayes optimal solution, which shows that the optimal model should reject to make predictions on the examples whose variance is larger than the rejection cost when the mean squared error is used as the evaluation metric. Furthermore, we propose to train the model by a surrogate loss function that considers rejection as binary classification and we provide conditions for the model consistency, which implies that the Bayes optimal solution can be recovered by our proposed surrogate loss. Extensive experiments demonstrate the effectiveness of our proposed method.

Uncertainty quantification (UQ) is a crucial but challenging task in many highdimensional learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that applies both to classical optimization approaches such as the LASSO as well as to neural networks. One of the most notable UQ techniques is the debiased LASSO, which modifies the LASSO to allow for the construction of asymptotic confidence intervals by decomposing the estimation error into a Gaussian and an asymptotically vanishing bias component. However, in real-world problems with finite-dimensional data, the bias term is often too significant to disregard, resulting in overly narrow confidence intervals. Our work rigorously addresses this issue and derives a data-driven adjustment that corrects the confidence intervals for a large class of predictors by estimating the means and variances of the bias terms from training data, exploiting high-dimensional concentration phenomena. This gives rise to non-asymptotic confidence intervals, which can help avoid overestimating certainty in critical applications such as MRI diagnosis. Importantly, our analysis extends beyond sparse regression to data-driven predictors like neural networks, enhancing the reliability of model-based deep learning. Our findings bridge the gap between established theory and the practical applicability of such methods.

In our proposed challenge, we draw from clinical pulsative waveform datasets to mimic mHealth pulsative waveforms, and in this section, we provide additional justification for this approach. A1.1 What is the rationale for constructing a dataset for mHealth signal imputation from equivalent signals connected in the clinical setting? While there are differences between clinical pulsative signals collected in a hospital setting and mHealth pulsative signals collected in the field, this was a necessary approach due to the scarcity of large, publicly-available mHealth datasets (e.g. PPG-DaLiA, an mHealth dataset, has 15 subjects whereas our curated MIMIC-III PPG dataset, derived from a clinical dataset, has 18,210 subjects). We can mimic real-world mHealth settings by applying realistic patterns of mHealth missingness. The original ablated samples are the ground truth, which makes it possible to quantify and visualize the imputation accuracy. A1.2 What are the differences in how the ECG/PPG sensors collect pulsative signals across both settings?