Rui Yao

Constantinos Daskalakis, Patroklos Stefanou, Rui Yao et al.

Truncated linear regression is a classical challenge in Statistics, wherein a label, $y = w^T x + \varepsilon$, and its corresponding feature vector, $x \in \mathbb{R}^k$, are only observed if the label falls in some subset $S \subseteq \mathbb{R}$; otherwise the existence of the pair $(x, y)$ is hidden from observation. Linear regression with truncated observations has remained a challenge, in its general form, since the early works of~\citet{tobin1958estimation,amemiya1973regression}. When the distribution of the error is normal with known variance, recent work of~\citet{daskalakis2019truncatedregression} provides computationally and statistically efficient estimators of the linear model, $w$. In this paper, we provide the first computationally and statistically efficient estimators for truncated linear regression when the noise variance is unknown, estimating both the linear model and the variance of the noise. Our estimator is based on an efficient implementation of Projected Stochastic Gradient Descent on the negative log-likelihood of the truncated sample. Importantly, we show that the error of our estimates is asymptotically normal, and we use this to provide explicit confidence regions for our estimates.

Rui Yao, Kai Sun, Feng Liu et al.

Since cascading outages are major threats to power systems, it is important to reduce the risk of potential cascading outages. In this paper, a risk management method of cascading outages based on Markovian tree search is proposed. With the tree expansion on the cascading outage risk, risk gradient is computed efficiently by a forward-backward tree search scheme with good convergence, and it is then employed in an optimization model to minimize control cost while effectively reducing the cascading outage risk. To overcome the limitation with linearization in computing risk gradient, an iterative risk management (IRM) approach is further developed. Tests on the RTS-96 3-area system verify the accuracy of the computed risk gradient and its effectiveness for risk reduction. Time performance of the proposed IRM approach is tested on the RTS-96 system, a 410-bus US-Canada northeast system and a 1354-bus Mid-European system, and demonstrates its potentials for decision support on practical power systems online or on hourly basis.

Constantinos Daskalakis, Vardis Kandiros, Rui Yao

We consider the problem of estimating Ising models over $n$ variables in Total Variation (TV) distance, given $l$ independent samples from the model. While the statistical complexity of the problem is well-understood [DMR20], identifying computationally and statistically efficient algorithms has been challenging. In particular, remarkable progress has occurred in several settings, such as when the underlying graph is a tree [DP21, BGPV21], when the entries of the interaction matrix follow a Gaussian distribution [GM24, CK24], or when the bulk of its eigenvalues lie in a small interval [AJK+24, KLV24], but no unified framework for polynomial-time estimation in TV exists so far. Our main contribution is a unified analysis of the Maximum Pseudo-Likelihood Estimator (MPLE) for two general classes of Ising models. The first class includes models that have bounded operator norm and satisfy the Modified Log-Sobolev Inequality (MLSI), a functional inequality that was introduced to study the convergence of the associated Glauber dynamics to stationarity. In the second class of models, the interaction matrix has bounded infinity norm (or bounded width), which is the most common assumption in the literature for structure learning of Ising models. We show how our general results for these classes yield polynomial-time algorithms and optimal or near-optimal sample complexity guarantees in a variety of settings. Our proofs employ a variety of tools from tensorization inequalities to measure decompositions and concentration bounds.

Yichen Zhang, Hantao Cui, Jianzhe Liu et al.

With the increasing penetration of renewable energy, frequency response and its security are of significant concerns for reliable power system operations. Frequency-constrained unit commitment (FCUC) is proposed to address this challenge. Despite existing efforts in modeling frequency characteristics in unit commitment (UC), current strategies can only handle oversimplified low-order frequency response models and do not consider wide-range operating conditions. This paper presents a generic data-driven framework for FCUC under high renewable penetration. Deep neural networks (DNNs) are trained to predict the frequency response using real data or high-fidelity simulation data. Next, the DNN is reformulated as a set of mixed-integer linear constraints to be incorporated into the ordinary UC formulation. In the data generation phase, all possible power injections are considered, and a region-of-interests active sampling is proposed to include power injection samples with frequency nadirs closer to the UFLC threshold, which significantly enhances the accuracy of frequency constraints in FCUC. The proposed FCUC is verified on the the IEEE 39-bus system. Then, a full-order dynamic model simulation using PSS/E verifies the effectiveness of FCUC in frequency-secure generator commitments.

Yichen Zhang, Jianzhe Liu, Feng Qiu et al.

Traditional methods for solvability region analysis can only have inner approximations with inconclusive conservatism. Machine learning methods have been proposed to approach the real region. In this letter, we propose a deep active learning framework for power system solvability prediction. Compared with the passive learning methods where the training is performed after all instances are labeled, the active learning selects most informative instances to be label and therefore significantly reduce the size of labeled dataset for training. In the active learning framework, the acquisition functions, which correspond to different sampling strategies, are defined in terms of the on-the-fly posterior probability from the classifier. The IEEE 39-bus system is employed to validate the proposed framework, where a two-dimensional case is illustrated to visualize the effectiveness of the sampling method followed by the full-dimensional numerical experiments.