**Inverse Conditional Probability Weighting (ICPW)**

Estimating the average treatment causal effect in clustered data often involves dealing with unmeasured cluster-specific confounding variables. Such variables may be correlated with the measured unit covariates and outcome. When the correlations are ignored, the causal effect estimation can be biased. By utilizing sufficient statistics, we propose an inverse conditional probability weighting (ICPW) method, which is robust to both (i) the correlation between the unmeasured cluster-specific confounding variable and the covariates and (ii) the correlation between the unmeasured cluster-specific confounding variable and the outcome. Assumptions and conditions for the ICPW method are presented. We establish the asymptotic properties of the proposed estimators. Simulation studies and a case study are presented for illustration. … **Embedded-Graph**

In this paper, we propose a new type of graph, denoted as ’embedded-graph’, and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated relations, which cannot be expressed by the existing edge-graphs or weighted-graphs. We introduce the mathematical definition of embedded-graph, translation, edge distance, and graph similarity. We can transform an embedded-graph into a weighted-graph and a weighted-graph into an edge-graph by the translation method and by threshold calculation, respectively. The edge distance of an embedded-graph is a distance based on the components of a target vector, and it is calculated through cosine similarity with the target vector. The graph similarity is obtained considering the relations with linguistic complexity. In addition, we provide some examples and data structures for embedded-graphs in this paper. … **Automatic Algorithm Discoverer (AAD)**

This paper presents Automatic Algorithm Discoverer (AAD), an evolutionary framework for synthesizing programs of high complexity. To guide evolution, prior evolutionary algorithms have depended on fitness (objective) functions, which are challenging to design. To make evolutionary progress, instead, AAD employs Problem Guided Evolution (PGE), which requires introduction of a group of problems together. With PGE, solutions discovered for simpler problems are used to solve more complex problems in the same group. PGE also enables several new evolutionary strategies, and naturally yields to High-Performance Computing (HPC) techniques. We find that PGE and related evolutionary strategies enable AAD to discover algorithms of similar or higher complexity relative to the state-of-the-art. Specifically, AAD produces Python code for 29 array/vector problems ranging from min, max, reverse, to more challenging problems like sorting and matrix-vector multiplication. Additionally, we find that AAD shows adaptability to constrained environments/inputs and demonstrates outside-of-the-box problem solving abilities. … **Anchors**

We introduce a novel model-agnostic system that explains the behavior of complex models with high-precision rules called anchors, representing local, ‘sufficient’ conditions for predictions. We propose an algorithm to efficiently compute these explanations for any black-box model with high-probability guarantees. We demonstrate the flexibility of anchors by explaining a myriad of different models for different domains and tasks. In a user study, we show that anchors enable users to predict how a model would behave on unseen instances with less effort and higher precision, as compared to existing linear explanations or no explanations. …

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