The Unit Commitment (UC) problem is a key optimization task in power systems to forecast the generation schedules of power units over a finite time period by minimizing costs while meeting demand and technical constraints. However, many parameters required by the UC problem are unknown, such as the costs. In this work, we estimate these unknown costs using simulation-based inference on an illustrative UC problem, which provides an approximated posterior distribution of the parameters given observed generation schedules and demands. Our results highlight that the learned posterior distribution effectively captures the underlying distribution of the data, providing a range of possible values for the unknown parameters given a past observation. This posterior allows for the estimation of past costs using observed past generation schedules, enabling operators to better forecast future costs and make more robust generation scheduling forecasts. We present avenues for future research to address overconfidence in posterior estimation, enhance the scalability of the methodology and apply it to more complex UC problems modeling the network constraints and renewable energy sources.

Queuing network control is essential for managing congestion in job-processing systems such as service systems, communication networks, and manufacturing processes. Despite growing interest in applying reinforcement learning (RL) techniques, queueing network control poses distinct challenges, including high stochasticity, large state and action spaces, and lack of stability. To tackle these challenges, we propose a scalable framework for policy optimization based on differentiable discrete event simulation. Our main insight is that by implementing a well-designed smoothing technique for discrete event dynamics, we can compute pathwise policy gradients for large-scale queueing networks using auto-differentiation software (e.g., Tensorflow, PyTorch) and GPU parallelization. Through extensive empirical experiments, we observe that our policy gradient estimators are several orders of magnitude more accurate than typical REINFORCE-based estimators. In addition, We propose a new policy architecture, which drastically improves stability while maintaining the flexibility of neural-network policies. In a wide variety of scheduling and admission control tasks, we demonstrate that training control policies with pathwise gradients leads to a 50-1000x improvement in sample efficiency over state-of-the-art RL methods. Unlike prior tailored approaches to queueing, our methods can flexibly handle realistic scenarios, including systems operating in non-stationary environments and those with non-exponential interarrival/service times.

The responses generated by Large Language Models (LLMs) can include sensitive information from individuals and organizations, leading to potential privacy leakage. This work implements Influence Functions (IFs) to trace privacy leakage back to the training data, thereby mitigating privacy concerns of Language Models (LMs). However, we notice that current IFs struggle to accurately estimate the influence of tokens with large gradient norms, potentially overestimating their influence. When tracing the most influential samples, this leads to frequently tracing back to samples with large gradient norm tokens, overshadowing the actual most influential samples even if their influences are well estimated. To address this issue, we propose Heuristically Adjusted IF (HAIF), which reduces the weight of tokens with large gradient norms, thereby significantly improving the accuracy of tracing the most influential samples. To establish easily obtained groundtruth for tracing privacy leakage, we construct two datasets, PII-E and PII-CR, representing two distinct scenarios: one with identical text in the model outputs and pre-training data, and the other where models leverage their reasoning abilities to generate text divergent from pre-training data. HAIF significantly improves tracing accuracy, enhancing it by 20.96% to 73.71% on the PII-E dataset and 3.21% to 45.93% on the PII-CR dataset, compared to the best SOTA IFs against various GPT-2 and QWen-1.5 models. HAIF also outperforms SOTA IFs on real-world pretraining data CLUECorpus2020, demonstrating strong robustness regardless prompt and response lengths.

Recent Vision Transformer (ViT)-based methods for Image Super-Resolution have demonstrated impressive performance. However, they suffer from significant complexity, resulting in high inference times and memory usage. Additionally, ViT models using Window Self-Attention (WSA) face challenges in processing regions outside their windows. To address these issues, we propose the Low-to-high Multi-Level Transformer (LMLT), which employs attention with varying feature sizes for each head. LMLT divides image features along the channel dimension, gradually reduces spatial size for lower heads, and applies self-attention to each head. This approach effectively captures both local and global information. By integrating the results from lower heads into higher heads, LMLT overcomes the window boundary issues in self-attention. Extensive experiments show that our model significantly reduces inference time and GPU memory usage while maintaining or even surpassing the performance of state-of-the-art ViT-based Image Super-Resolution methods. Our codes are availiable at https://github.com/jwgdmkj/LMLT.

We consider the overfitting behavior of minimum norm interpolating solutions of Gaussian kernel ridge regression (i.e. kernel ridgeless regression), when the bandwidth or input dimension varies with the sample size. For fixed dimensions, we show that even with varying or tuned bandwidth, the ridgeless solution is never consistent and, at least with large enough noise, always worse than the null predictor. For increasing dimension, we give a generic characterization of the overfitting behavior for any scaling of the dimension with sample size. We use this to provide the first example of benign overfitting using the Gaussian kernel with sub-polynomial scaling dimension. All our results are under the Gaussian universality ansatz and the (non-rigorous) risk predictions in terms of the kernel eigenstructure.

We introduce a general iterative procedure called risk-based calibration (RC) designed to minimize the empirical risk under the 0-1 loss (empirical error) for probabilistic classifiers. These classifiers are based on modeling probability distributions, including those constructed from the joint distribution (generative) and those based on the class conditional distribution (conditional). RC can be particularized to any probabilistic classifier provided a specific learning algorithm that computes the classifier's parameters in closed form using data statistics. RC reinforces the statistics aligned with the true class while penalizing those associated with other classes, guided by the 0-1 loss. The proposed method has been empirically tested on 30 datasets using na\"ive Bayes, quadratic discriminant analysis, and logistic regression classifiers. RC improves the empirical error of the original closed-form learning algorithms and, more notably, consistently outperforms the gradient descent approach with the three classifiers.

Learning new tasks by drawing on prior experience gathered from other (related) tasks is a core property of any intelligent system. Gradient-based meta-learning, especially MAML and its variants, has emerged as a viable solution to accomplish this goal. One problem MAML encounters is its computational and memory burdens needed to compute the meta-gradients. We propose a new first-order variant of MAML that we prove converges to a stationary point of the MAML objective, unlike other first-order variants. We also show that the MAML objective does not satisfy the smoothness assumption assumed in previous works; we show instead that its smoothness constant grows with the norm of the meta-gradient, which theoretically suggests the use of normalized or clipped-gradient methods compared to the plain gradient method used in previous works.

Automatic Medical Imaging Narrative generation aims to alleviate the workload of radiologists by producing accurate clinical descriptions directly from radiological images. However, the subtle visual nuances and domain-specific terminology in medical images pose significant challenges compared to generic image captioning tasks. Existing approaches often neglect the vital distinction between normal and abnormal findings, leading to suboptimal performance. In this work, we propose FODA-PG, a novel Fine-grained Organ-Disease Adaptive Partitioning Graph framework that addresses these limitations through domain-adaptive learning. FODA-PG constructs a granular graphical representation of radiological findings by separating disease-related attributes into distinct "disease-specific" and "disease-free" categories based on their clinical significance and location. This adaptive partitioning enables our model to capture the nuanced differences between normal and pathological states, mitigating the impact of data biases. By integrating this fine-grained semantic knowledge into a powerful transformer-based architecture and providing rigorous mathematical justifications for its effectiveness, FODA-PG generates precise and clinically coherent reports with enhanced generalization capabilities. Extensive experiments on the IU-Xray and MIMIC-CXR benchmarks demonstrate the superiority of our approach over state-of-the-art methods, highlighting the importance of domain adaptation in medical report generation.

Matrix completion tackles the task of predicting missing values in a low-rank matrix based on a sparse set of observed entries. It is often assumed that the observation pattern is generated uniformly at random or has a very specific structure tuned to a given algorithm. There is still a gap in our understanding when it comes to arbitrary sampling patterns. Given an arbitrary sampling pattern, we introduce a matrix completion algorithm based on network flows in the bipartite graph induced by the observation pattern. For additive matrices, the particular flow we used is the electrical flow and we establish error upper bounds customized to each entry as a function of the observation set, along with matching minimax lower bounds. Our results show that the minimax squared error for recovery of a particular entry in the matrix is proportional to the effective resistance of the corresponding edge in the graph. Furthermore, we show that our estimator is equivalent to the least squares estimator. We apply our estimator to the two-way fixed effects model and show that it enables us to accurately infer individual causal effects and the unit-specific and time-specific confounders. For rank-$1$ matrices, we use edge-disjoint paths to form an estimator that achieves minimax optimal estimation when the sampling is sufficiently dense. Our discovery introduces a new family of estimators parametrized by network flows, which provide a fine-grained and intuitive understanding of the impact of the given sampling pattern on the relative difficulty of estimation at an entry-specific level. This graph-based approach allows us to quantify the inherent complexity of matrix completion for individual entries, rather than relying solely on global measures of performance.

In this work we explore parsimonious manifold learning techniques, specifically for Diffusion-maps. We demonstrate an algorithm and it's implementation with computational complexity (in both time and memory) of $\sim N$, with $N$ representing the number-of-samples. These techniques are essential for large-scale unsupervised learning tasks without any prior assumptions, due to sampling theorem limitations.