In online selective conformal inference, data arrives sequentially, and prediction intervals are constructed only when an online selection rule is met. Since online selections may break the exchangeability between the selected test datum and the rest of the data, one must correct for this by suitably selecting the calibration data. In this paper, we evaluate existing calibration selection strategies and pinpoint some fundamental errors in the associated claims that guarantee selection-conditional coverage and control of the false coverage rate (FCR). To address these shortcomings, we propose novel calibration selection strategies that provably preserve the exchangeability of the calibration data and the selected test datum. Consequently, we demonstrate that online selective conformal inference with these strategies guarantees both selection-conditional coverage and FCR control. Our theoretical findings are supported by experimental evidence examining tradeoffs between valid methods.

In supervised learning, including regression and classification, conformal methods provide prediction sets for the outcome/label with finite sample coverage for any machine learning predictor. We consider here the case where such prediction sets come after a selection process. The selection process requires that the selected prediction sets be `informative' in a well defined sense. We consider both the classification and regression settings where the analyst may consider as informative only the sample with prediction sets small enough, excluding null values, or obeying other appropriate `monotone' constraints. We develop a unified framework for building such informative conformal prediction sets while controlling the false coverage rate (FCR) on the selected sample. While conformal prediction sets after selection have been the focus of much recent literature in the field, the new introduced procedures, called InfoSP and InfoSCOP, are to our knowledge the first ones providing FCR control for informative prediction sets. We show the usefulness of our resulting procedures on real and simulated data.

We study the problem of post-selection predictive inference in an online fashion. To avoid devoting resources to unimportant units, a preliminary selection of the current individual before reporting its prediction interval is common and meaningful in online predictive tasks. Since the online selection causes a temporal multiplicity in the selected prediction intervals, it is important to control the real-time false coverage-statement rate (FCR) to measure the averaged miscoverage error. We develop a general framework named CAS (Calibration after Adaptive Selection) that can wrap around any prediction model and online selection rule to output post-selection prediction intervals. If the current individual is selected, we first perform an adaptive selection on historical data to construct a calibration set, then output a conformal prediction interval for the unobserved label. We provide tractable constructions for the calibration set for popular online selection rules. We proved that CAS can achieve an exact selection-conditional coverage guarantee in the finite-sample and distribution-free regimes. For the decision-driven selection rule, including most online multiple-testing procedures, CAS can exactly control the real-time FCR below the target level without any distributional assumptions. For the online selection with symmetric thresholds, we establish the error bound for the control gap of FCR under mild distributional assumptions. To account for the distribution shift in online data, we also embed CAS into some recent dynamic conformal prediction methods and examine the long-run FCR control. Numerical results on both synthetic and real data corroborate that CAS can effectively control FCR around the target level and yield more narrowed prediction intervals over existing baselines across various settings.

Large language models (LLMs) have shown impressive performance in various reasoning benchmarks with the emergence of Chain-of-Thought (CoT) and its derivative methods, particularly in tasks involving multi-choice questions (MCQs). However, current works all process data uniformly without considering the problem-solving difficulty, which means an excessive focus on simple questions while insufficient to intricate ones. To address this challenge, we inspired by humans using heuristic strategies to categorize tasks and handle them individually, propose to apply the Divide and Conquer to LLMs reasoning. First, we divide questions into different subsets based on the statistical confidence score ($\mathcal{CS}$), then fix nearly resolved sets and conquer demanding nuanced process ones with elaborately designed methods, including Prior Knowledge based Reasoning (PKR) and Filter Choices based Reasoning (FCR), as well as their integration variants. Our experiments demonstrate that this proposed strategy significantly boosts the models' reasoning abilities across nine datasets involving arithmetic, commonsense, and logic tasks. For instance, compared to baseline, we make a striking improvement on low confidence subsets of 8.72\% for AQuA, 15.07\% for ARC Challenge and 7.71\% for RiddleSense. In addition, through extensive analysis on length of rationale and number of options, we verify that longer reasoning paths in PKR could prevent models from referring infer-harmful shortcuts, and also find that removing irrelevant choices in FCR would substantially avoid models' confusion. The code is at \url{https://github.com/AiMijie/Divide-and-Conquer}

Nonparametric two-sample tests such as the Maximum Mean Discrepancy (MMD) are often used to detect differences between two distributions in machine learning applications. However, the majority of existing literature assumes that error-free samples from the two distributions of interest are available.We relax this assumption and study the estimation of the MMD under $\epsilon$-contamination, where a possibly non-random $\epsilon$ proportion of one distribution is erroneously grouped with the other. We show that under $\epsilon$-contamination, the typical estimate of the MMD is unreliable. Instead, we study partial identification of the MMD, and characterize sharp upper and lower bounds that contain the true, unknown MMD. We propose a method to estimate these bounds, and show that it gives estimates that converge to the sharpest possible bounds on the MMD as sample size increases, with a convergence rate that is faster than alternative approaches. Using three datasets, we empirically validate that our approach is superior to the alternatives: it gives tight bounds with a low false coverage rate.

Perfusion imaging is a valuable tool for diagnosing and treatment planning for liver tumours. The time separation technique (TST) has been successfully used for modelling C-arm cone-beam computed tomography (CBCT) perfusion data. The reconstruction can be accompanied by the segmentation of the liver - for better visualisation and for generating comprehensive perfusion maps. Recently introduced Turbolift learning has been seen to perform well while working with TST reconstructions, but has not been explored for the time-resolved volumes (TRV) estimated out of TST reconstructions. The segmentation of the TRVs can be useful for tracking the movement of the liver over time. This research explores this possibility by training the multi-scale attention UNet of Turbolift learning at its third stage on the TRVs and shows the robustness of Turbolift learning since it can even work efficiently with the TRVs, resulting in a Dice score of 0.864$\pm$0.004.

Estimation of individual treatment effects is often used as the basis for contextual decision making in fields such as healthcare, education, and economics. However, in many real-world applications it is sufficient for the decision maker to have upper and lower bounds on the potential outcomes of decision alternatives, allowing them to evaluate the trade-off between benefit and risk. With this in mind, we develop an algorithm for directly learning upper and lower bounds on the potential outcomes under treatment and non-treatment. Our theoretical analysis highlights a trade-off between the complexity of the learning task and the confidence with which the resulting bounds cover the true potential outcomes; the more confident we wish to be, the more complex the learning task is. We suggest a novel algorithm that maximizes a utility function while maintaining valid potential outcome bounds. We illustrate different properties of our algorithm, and highlight how it can be used to guide decision making using two semi-simulated datasets.

Building on my April 2018 column "Using AI, Bots, Big Data, and Analytics to Reduce Demand for Support"1, one of the seven vexing challenges facing customer experience (CX) leaders, today I'll address the second challenge to increase First Contact Resolution (FCR). The power of AI, bots, Big Data, and analytics can now enable us to address the overall goal "How can we create and sustain a consistent and awesome customer experience across multiple channels & touch points?" and thereby increase sustainable revenues, realize higher margins, and sustain greater levels of customer satisfaction and loyalty. Let's dig into the second challenge, Increase FCR. Study after study has confirmed that first contact resolution in the contact center and other support functions is the biggest driver of customer satisfaction2. However, most companies rely overly much on point statistics like average FCR, and they neglect the fact that customers today start their inquiry or search for support online, failing that in the IVR system, only to find themselves speaking, emailing, or chatting with a customer service agent.