Conformal prediction provides rigorous distribution-free finite-sample guarantees for marginal coverage under the assumption of exchangeability, but may exhibit systematic undercoverage or overcoverage for specific subpopulations. Assessing conditional validity is challenging, as standard stratification methods suffer from the curse of dimensionality. We propose Conformal Prediction Assessment (CPA), a framework that reframes the evaluation of conditional coverage as a supervised learning task by training a reliability estimator that predicts instance-level coverage probabilities. Building on this estimator, we introduce the Conditional Validity Index (CVI), which decomposes reliability into safety (undercoverage risk) and efficiency (overcoverage cost). We establish convergence rates for the reliability estimator and prove the consistency of CVI-based model selection. Extensive experiments on synthetic and real-world datasets demonstrate that CPA effectively diagnoses local failure modes and that CC-Select, our CVI-based model selection algorithm, consistently identifies predictors with superior conditional coverage performance.

The CF of a random variable (r.v.) is the Fourier transform of its probability distribution function (PDF).

City leaders face critical decisions regarding budget allocation and investment priorities. How can they identify which city districts require revitalization? To address this challenge, a Current Vitality Index and a Long-Term Vitality Index are proposed. These indexes are based on a carefully curated set of indicators. Missing data is handled using K-Nearest Neighbors imputation, while Random Forest is employed to identify the most reliable and significant features. Additionally, k-means clustering is utilized to generate meaningful data groupings for enhanced monitoring of Long-Term Vitality. Current vitality is visualized through an interactive map, while Long-Term Vitality is tracked over 15 years with predictions made using Multilayer Perceptron or Linear Regression. The results, approved by urban planners, are already promising and helpful, with the potential for further improvement as more data becomes available. This paper proposes leveraging machine learning methods to optimize urban planning and enhance citizens' quality of life.

A vast number of different methods are available for unsupervised classification. Since no algorithm and parameter setting performs best in all types of data, there is a need for cluster validation to select the actually best-performing algorithm. Several indices were proposed for this purpose without using any additional (external) information. These internal validation indices can be evaluated by applying them to classifications of datasets with a known cluster structure. Evaluation approaches differ in how they use the information on the ground-truth classification. This paper reviews these approaches, considering their advantages and disadvantages, and then suggests a new approach.

Abstract: We employ unsupervised machine learning to enhance the accuracy of our recently presented scaling method for wave confinement analysis [1]. We employ the standard k-means++ algorithm as well as our own model-based algorithm. We investigate cluster validity indices as a means to find the correct number of confinement dimensionalities to be used as an input to the clustering algorithms. Subsequently, we analyze the performance of the two clustering algorithms when compared to the direct application of the scaling method without clustering. We find that the clustering approach provides more physically meaningful results, but may struggle with identifying the correct set of confinement dimensionalities. We conclude that the most accurate outcome is obtained by first applying the direct scaling to find the correct set of confinement dimensionalities and subsequently employing clustering to refine the results. Moreover, our model-based algorithm outperforms the standard k-means++ clustering. 1. Introduction Completely controlling wave propagation in periodic media is a key challenge that is essential for a large variety of applications [2-16]. An especially interesting type of control is wave confinement achieved by introducing disorder and functional defects into an otherwise periodic medium [17-20]. The interference of waves in such an altered structure may result in a strong concentration of the energy density inside a small sub-volume of the medium. Wave confinement has been investigated for different types of waves and in various settings, e.g., classical mechanics [21], photonics [10, 11, 22-24], solid state physics [25-29], or magnonics [30, 31]. Its applications include sensors, controlled spontaneous emission, and enhanced interactions between hybrid wave-types such as sound and light [32-40].

In real-world decision-making, uncertainty is important yet difficult to handle. Stochastic dominance provides a theoretically sound approach for comparing uncertain quantities, but optimization with stochastic dominance constraints is often computationally expensive, which limits practical applicability. In this paper, we develop a simple yet efficient approach for the problem, the Light Stochastic Dominance Solver (light-SD), that leverages useful properties of the Lagrangian. We recast the inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses apparent intractability and leads to tractable updates or even closed-form solutions for gradient calculations. We prove convergence of the algorithm and test it empirically. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.

This work studies efficient solution methods for cluster-based control policies of transition-independent Markov decision processes (TI-MDPs). We focus on control of multi-agent systems, whereby a central planner (CP) influences agents to select desirable group behavior. The agents are partitioned into disjoint clusters whereby agents in the same cluster receive the same controls but agents in different clusters may receive different controls. Under mild assumptions, this process can be modeled as a TI-MDP where each factor describes the behavior of one cluster. The action space of the TI-MDP becomes exponential with respect to the number of clusters. To efficiently find a policy in this rapidly scaling space, we propose a clustered Bellman operator that optimizes over the action space for one cluster at any evaluation. We present Clustered Value Iteration (CVI), which uses this operator to iteratively perform "round robin" optimization across the clusters. CVI converges exponentially faster than standard value iteration (VI), and can find policies that closely approximate the MDP's true optimal value. A special class of TI-MDPs with separable reward functions are investigated, and it is shown that CVI will find optimal policies on this class of problems. Finally, the optimal clustering assignment problem is explored. The value functions TI-MDPs with submodular reward functions are shown to be submodular functions, so submodular set optimization may be used to find a near optimal clustering assignment. We propose an iterative greedy cluster splitting algorithm, which yields monotonic submodular improvement in value at each iteration. Finally, simulations offer empirical assessment of the proposed methods.

Network economics is the study of a rich class of equilibrium problems that occur in the real world, from traffic management to supply chains and two-sided online marketplaces. In this paper we explore causal inference in network economics, building on the mathematical framework of variational inequalities, which is a generalization of classical optimization. Our framework can be viewed as a synthesis of the well-known variational inequality formalism with the broad principles of causal inference.

To evaluate clustering results is a significant part in cluster analysis. Usually, there is no true class labels for clustering as a typical unsupervised learning. Thus, a number of internal evaluations, which use predicted labels and data, have been created. They also named internal cluster validity indices (CVIs). Without true labels, to design an effective CVI is not simple because it is similar to create a clustering method. And, to have more CVIs is crucial because there is no universal CVI that can be used to measure all datasets, and no specific method for selecting a proper CVI for clusters without true labels. Therefore, to apply more CVIs to evaluate clustering results is necessary. In this paper, we propose a novel CVI - called Distance-based Separability Index (DSI), based on a data separability measure. We applied the DSI and eight other internal CVIs including early studies from Dunn (1974) to most recent studies CVDD (2019) as comparison. We used an external CVI as ground truth for clustering results of five clustering algorithms on 12 real and 97 synthetic datasets. Results show DSI is an effective, unique, and competitive CVI to other compared CVIs. In addition, we summarized the general process to evaluate CVIs and created a new method - rank difference - to compare the results of CVIs.

Continuous V alue Iteration (CVI) Reinforcement Learning and Imaginary Experience Replay (IER) for learning multi-goal, continuous action and state space controllers Andreas Gerken and Michael Spranger Sony Computer Science Laboratories Inc., Tokyo, Japan Abstract -- This paper presents a novel model-free Reinforcement Learning algorithm for learning behavior in continuous action, state, and goal spaces. The algorithm approximates optimal value functions using nonparametric estimators. It is able to efficiently learn to reach multiple arbitrary goals in deterministic and nondeterministic environments. T o improve generalization in the goal space, we propose a novel sample augmentation technique. Using these methods, robots learn faster and overall better controllers. We benchmark the proposed algorithms using simulation and a real-world voltage controlled robot that learns to maneuver in a non-observable Cartesian task space. I NTRODUCTION Learning to control one's body is a crucial skill for any embodied agent. A common way of framing the problem of learning to control an agent is Reinforcement Learning (RL). RL poses the problem in terms of actions that an agent can perform, observed states of the world and some reward function that pays out a treat or punishes the agent depending on its performance. The aim of an optimal RL controller is to maximize the collected rewards. Reinforcement Learning has been studied widely and applied to different domains of learning and control.