Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a realized conformal threshold. In the continuous i.i.d. setting this law is exactly $Beta(k,n+1-k)$, so the usual marginal guarantee corresponds to its mean. We take this beta law as a finite-sample reference object and quantify departures from it using Wasserstein distances on $[0,1]$. The framework yields direct bounds on marginal coverage gaps and on bad-calibration probabilities, and separates different sources of non-i.i.d. behavior according to how they deform the beta reference: test-side shift acts through a transport map on the coverage scale, while calibration dependence changes the order-statistic law itself. We instantiate the framework in scale-shift, clustered, and stationary mixing settings, where the induced deformations can be characterized explicitly or through Berry-Esseen approximations. Simulations on dependent processes confirm that the first-order approximation tracks the empirical Wasserstein distance even at moderate sample sizes.

I've recently introduced a few friends to the power of a great robot vacuum. One of my friends calls hers a marriage saver, while the other was both thrilled and horrified by how many stains the vacuum's AI found on her floors. Personally, my robot vacuums keep me from wanting to set the litter box on fire, since my cat is on a mission to create his own navigational trail of litter through my home. The best robot vacuums these days aren't just vacuuming your floors, nor are they blindly bumping around your house like they used to. These gadgets are mopping, scrubbing away stains, lifting themselves off of obstacles, and even reminding you to clean the dirtier areas in your home more frequently. A good robot vacuum can cost a pretty penny, but it doesn't have to, depending on what you're looking for. I've been testing every new robot vacuum I can in my three-story home filled with three adults, a preschooler, and a cat who's on a mission to get litter all over the house.

Quantum Machine Learning (QML) holds the promise of enhancing machine learning modeling in terms of both complexity and accuracy. A key challenge in this domain is the encoding of input data, which plays a pivotal role in determining the performance of QML models. In this work, we tackle a largely unaddressed aspect of encoding that is unique to QML modeling -- rather than adjusting the ansatz used for encoding, we consider adjusting how data is conveyed to the ansatz. We specifically implement QML pipelines that leverage classical data manipulation (i.e., ordering, selecting, and weighting features) as a preprocessing step, and evaluate if these aspects of encoding can have a significant impact on QML model performance, and if they can be effectively optimized to improve performance. Our experimental results, applied across a wide variety of data sets, ansatz, and circuit sizes, with a representative QML approach, demonstrate that by optimizing how features are encoded in an ansatz we can substantially and consistently improve the performance of QML models, making a compelling case for integrating these techniques in future QML applications. Finally we demonstrate the practical feasibility of this approach by running it using real quantum hardware with 100 qubit circuits and successfully achieving improved QML modeling performance in this case as well.

Things to Do in L.A. Tap to enable a layout that focuses on the article. Homework faces an existential crisis. Has AI made it pointless? Students wait for a celebration of high test scores to begin at La Tijera Academy of Excellence in Inglewood on Wednesday. This is read by an automated voice.

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Decision trees are a commonly used class of machine learning models valued for their interpretability and versatility, capable of both classification and regression. We propose ZTree, a novel decision tree learning framework that replaces CART's traditional purity based splitting with statistically principled subgroup identification. At each node, ZTree applies hypothesis testing (e.g., z-tests, t-tests, Mann-Whitney U, log-rank) to assess whether a candidate subgroup differs meaningfully from the complement. To adjust for the complication of multiple testing, we employ a cross-validation-based approach to determine if further node splitting is needed. This robust stopping criterion eliminates the need for post-pruning and makes the test threshold (z-threshold) the only parameter for controlling tree complexity. Because of the simplicity of the tree growing procedure, once a detailed tree is learned using the most lenient z-threshold, all simpler trees can be derived by simply removing nodes that do not meet the larger z-thresholds. This makes parameter tuning intuitive and efficient. Furthermore, this z-threshold is essentially a p-value, allowing users to easily plug in appropriate statistical tests into our framework without adjusting the range of parameter search. Empirical evaluation on five large-scale UCI datasets demonstrates that ZTree consistently delivers strong performance, especially at low data regimes. Compared to CART, ZTree also tends to grow simpler trees without sacrificing performance. ZTree introduces a statistically grounded alternative to traditional decision tree splitting by leveraging hypothesis testing and a cross-validation approach to multiple testing correction, resulting in an efficient and flexible framework.

We introduce the Markov missing graph (MMG), a novel framework that imputes missing data based on undirected graphs. MMG leverages conditional independence relationships to locally decompose the imputation model. To establish the identification, we introduce the Principle of Available Information (PAI), which guides the use of all relevant observed data. We then propose a flexible statistical learning paradigm, MMG Imputation Risk Minimization under PAI, that frames the imputation task as an empirical risk minimization problem. This framework is adaptable to various modeling choices. We develop theories of MMG, including the connection between MMG and Little's complete-case missing value assumption, recovery under missing completely at random, efficiency theory, and graph-related properties. We show the validity of our method with simulation studies and illustrate its application with a real-world Alzheimer's data set.

When adopting the role of a teacher in learning-by-teaching environments, students often struggle to engage in knowledge-building activities, such as providing explanations and addressing misconceptions. Instead, they frequently default to knowledge-telling behaviors, where they simply dictate what they already know or what to do without deeper reflection, thereby limiting learning. Teachable agents, particularly those capable of posing persistent follow-up questions, have been shown to encourage students (tutors) to shift from knowledge-telling to knowledge-building and enhance tutor learning. Tutor learning encompasses two interrelated types of knowledge: conceptual and procedural knowledge. Research has established a bidirectional relationship between these knowledge types, where improvements in one reinforce the other. This study investigates the role of knowledge-building in mediating the bidirectional relationship between procedural and conceptual learning. Our findings revealed a stable bidirectional relationship between procedural and conceptual knowledge, with higher post-test scores observed among students who engaged in knowledge-building, regardless of their procedural and conceptual pre-test performance. This suggests that knowledge-building serves as a crucial mechanism bridging the gap between students with low prior knowledge and higher conceptual and procedural learning gain.

The green lines in Figure 1 demonstrate that the stiffness decreases as the number of training levels increases in most of the Procgen games. This suggests that the delayed critic update effectively alleviates the memorization problem. Each agent is trained on 200 training levels for 25M environment steps. Each agent is trained for 8M environment steps. The mean is computed over 10 different runs.