We thank the reviewers and the editor for their reviews and helpful comments, which will improve our manuscript. We take seriously R2's suggestion to change our method's acronym and thank him/her for pointing out We have also followed the reviewer's suggestion to illustrate We have added this example to our manuscript. This is obviously true and is noted in Section 5 of the manuscript. We cannot put it better than R2: "although it [the use of quantile regression] This is the main point of our paper. In particular, why estimate the mean if the goal is to estimate quantiles?

Uncertainty quantification is essential in decision-making, especially when joint distributions of random variables are involved. While conformal prediction provides distribution-free prediction sets with valid coverage guarantees, it traditionally focuses on single predictions. This paper introduces novel conformal prediction methods for estimating the sum or average of unknown labels over specific index sets. We develop conformal prediction intervals for single target to the prediction interval for sum of multiple targets. Under permutation invariant assumptions, we prove the validity of our proposed method. We also apply our algorithms on class average estimation and path cost prediction tasks, and we show that our method outperforms existing conformalized approaches as well as non-conformal approaches.

Predicting the minimum operating voltage ($V_{min}$) of chips is one of the important techniques for improving the manufacturing testing flow, as well as ensuring the long-term reliability and safety of in-field systems. Current $V_{min}$ prediction methods often provide only point estimates, necessitating additional techniques for constructing prediction confidence intervals to cover uncertainties caused by different sources of variations. While some existing techniques offer region predictions, but they rely on certain distributional assumptions and/or provide no coverage guarantees. In response to these limitations, we propose a novel distribution-free $V_{min}$ interval estimation methodology possessing a theoretical guarantee of coverage. Our approach leverages conformalized quantile regression and on-chip monitors to generate reliable prediction intervals. We demonstrate the effectiveness of the proposed method on an industrial 5nm automotive chip dataset. Moreover, we show that the use of on-chip monitors can reduce the interval length significantly for $V_{min}$ prediction.

As an autonomous system performs a task, it should maintain a calibrated estimate of the probability that it will achieve the user's goal. If that probability falls below some desired level, it should alert the user so that appropriate interventions can be made. This paper considers settings where the user's goal is specified as a target interval for a real-valued performance summary, such as the cumulative reward, measured at a fixed horizon $H$. At each time $t \in \{0, \ldots, H-1\}$, our method produces a calibrated estimate of the probability that the final cumulative reward will fall within a user-specified target interval $[y^-,y^+].$ Using this estimate, the autonomous system can raise an alarm if the probability drops below a specified threshold. We compute the probability estimates by inverting conformal prediction. Our starting point is the Conformalized Quantile Regression (CQR) method of Romano et al., which applies split-conformal prediction to the results of quantile regression. CQR is not invertible, but by using the conditional cumulative distribution function (CDF) as the non-conformity measure, we show how to obtain an invertible modification that we call \textbf{P}robability-space \textbf{C}onformalized \textbf{Q}uantile \textbf{R}egression (PCQR). Like CQR, PCQR produces well-calibrated conditional prediction intervals with finite-sample marginal guarantees. By inverting PCQR, we obtain marginal guarantees for the probability that the cumulative reward of an autonomous system will fall within an arbitrary user-specified target intervals. Experiments on two domains confirm that these probabilities are well-calibrated.

Context-dependent text-to-SQL is the task of translating multi-turn questions into database-related SQL queries. Existing methods typically focus on making full use of history context or previously predicted SQL for currently SQL parsing, while neglecting to explicitly comprehend the schema and conversational dependency, such as co-reference, ellipsis and user focus change. In this paper, we propose CQR-SQL, which uses auxiliary Conversational Question Reformulation (CQR) learning to explicitly exploit schema and decouple contextual dependency for SQL parsing. Specifically, we first present a schema enhanced recursive CQR method to produce domain-relevant self-contained questions. Secondly, we train CQR-SQL models to map the semantics of multi-turn questions and auxiliary self-contained questions into the same latent space through schema grounding consistency task and tree-structured SQL parsing consistency task, which enhances the abilities of SQL parsing by adequately contextual understanding. At the time of writing, our CQR-SQL achieves new state-of-the-art results on two context-dependent text-to-SQL benchmarks SParC and CoSQL.

CQRS stands for Command Query Responsibility Segregation. It's a pattern that I first heard described by Greg Young. At its heart is the notion that you can use a different model to update information than the model you use to read information. For some situations, this separation can be valuable, but beware that for most systems CQRS adds risky complexity. The mainstream approach people use for interacting with an information system is to treat it as a CRUD datastore.

Matteo Sesia 1 and Emmanuel J. Cand es 1,2 1 Department of Statistics, Stanford University 2 Department of Mathematics, Stanford University September 13, 2019 Abstract We compare two recently proposed methods that combine ideas from conformal inference and quantile regression to produce locally adaptive and marginally valid prediction intervals under sample exchangeability (Romano et al., 2019 [1]; Kivaranovic et al., 2019 [2]). First, we prove that these two approaches are asymptotically efficient in large samples, under some additional assumptions. Then we compare them empirically on simulated and real data. Our results demonstrate that the method in Romano et al. (2019) typically yields tighter prediction intervals in finite samples. Finally, we discuss how to tune these procedures by fixing the relative proportions of observations used for training and conformalization. 1 Introduction 1.1 Background and motivation Given a set of n points { (X i,Y i) } n i 1, with Y i R and X i R d, we consider the problem of constructing a prediction interval for a new point Y n 1based on the observed value of X n 1, assuming only that { (X i,Y i) } n 1 i 1 are drawn exchangeably from some common distribution P XY. There exist a vast selection of statistical and machine learning algorithms that can provide approximate answers to this question [3, 4].