Causal discovery aims to infer causal graphs from observational or experimental data. Methods such as the popular PC algorithm are based on conditional independence testing and utilize enabling assumptions, such as the faithfulness assumption, for their inferences. In practice, these assumptions, as well as the functional assumptions inherited from the chosen conditional independence test, are typically taken as a given and not further tested for their validity on the data. In this work, we propose internal coherency scores that allow testing for assumption violations and finite sample errors, whenever detectable without requiring ground truth or further statistical tests. We provide a complete classification of erroneous results, including a distinction between detectable and undetectable errors, and prove that the detectable erroneous results can be measured by our scores. We illustrate our coherency scores on the PC algorithm with simulated and real-world datasets, and envision that testing for internal coherency can become a standard tool in applying constraint-based methods, much like a suite of tests is used to validate the assumptions of classical regression analysis.

Search is a prominent channel for discovering products on an e-commerce platform. Ranking products retrieved from search becomes crucial to address customer's need and optimize for business metrics. While learning to Rank (LETOR) models have been extensively studied and have demonstrated efficacy in the context of web search; it is a relatively new research area to be explored in the e-commerce. In this paper, we present a framework for building LETOR model for an e-commerce platform. We analyze user queries and propose a mechanism to segment queries between broad and narrow based on user's intent. We discuss different types of features - query, product and query-product and discuss challenges in using them. We show that sparsity in product features can be tackled through a denoising auto-encoder while skip-gram based word embeddings help solve the query-product sparsity issues. We also present various target metrics that can be employed for evaluating search results and compare their robustness. Further, we build and compare performances of both pointwise and pairwise LETOR models on fashion category data set. We also build and compare distinct models for broad and narrow queries, analyze feature importance across these and show that these specialized models perform better than a combined model in the fashion world.