Source coding is the canonical problem of data compression in information theory. In a locally encodable source coding, each compressed bit depends on only few bits of the input.

The notion of cause, as formalized by Halpern and Pearl, has been recently applied to relational databases, to characterize and compute causal explanations for query answers. In this work we consider the alternative notion of sufficient explanation. We investigate its connections with database repairs as used for dealing with inconsistent databases, and with causality-based necessary explanations. We also obtain some computational results.

A significant use case of instruction-finetuned Large Language Models (LLMs) is to solve question-answering tasks interactively. In this setting, an LLM agent is tasked with making a prediction by sequentially querying relevant information from the user, as opposed to a single-turn conversation. This paper explores sequential querying strategies that aim to minimize the expected number of queries. One such strategy is Information Pursuit (IP), a greedy algorithm that at each iteration selects the query that maximizes information gain or equivalently minimizes uncertainty. However, obtaining accurate estimates of mutual information or conditional entropy for LLMs is very difficult in practice due to over- or under-confident LLM probabilities, which leads to suboptimal query selection and predictive performance. To better estimate the uncertainty at each iteration, we propose Conformal Information Pursuit (C-IP), an alternative approach to sequential information gain based on conformal prediction sets. More specifically, C-IP leverages a relationship between prediction sets and conditional entropy at each iteration to estimate uncertainty based on the average size of conformal prediction sets. In contrast to conditional entropy, we find that conformal prediction sets are a distribution-free and robust method of measuring uncertainty. Experiments with 20 Questions show that C-IP obtains better predictive performance and shorter query-answer chains compared to previous approaches to IP and uncertainty-based chain-of-thought methods. Furthermore, extending to an interactive medical setting between a doctor and a patient on the MediQ dataset, C-IP achieves competitive performance with direct single-turn prediction while offering greater interpretability.

This work studies the applicability of expensive external oracles such as large language models in answering top-k queries over predicted scores. Such scores are incurred by user-defined functions to answer personalized queries over multi-modal data. We propose a generic computational framework that handles arbitrary set-based scoring functions, as long as the functions could be decomposed into constructs, each of which sent to an oracle (in our case an LLM) to predict partial scores. At a given point in time, the framework assumes a set of responses and their partial predicted scores, and it maintains a collection of possible sets that are likely to be the true top-k. Since calling oracles is costly, our framework judiciously identifies the next construct, i.e., the next best question to ask the oracle so as to maximize the likelihood of identifying the true top-k. We present a principled probabilistic model that quantifies that likelihood. We study efficiency opportunities in designing algorithms. We run an evaluation with three large scale datasets, scoring functions, and baselines. Experiments indicate the efficacy of our framework, as it achieves an order of magnitude improvement over baselines in requiring LLM calls while ensuring result accuracy. Scalability experiments further indicate that our framework could be used in large-scale applications.

Query answering over data with dependencies plays a central role in most applications of dependencies. The problem is commonly solved by using a suitable variant of the chase algorithm to compute a universal model of the dependencies and the data and thus explicate all knowledge implicit in the dependencies. After this preprocessing step, an arbitrary conjunctive query over the dependencies and the data can be answered by evaluating it the computed universal model. If, however, the query to be answered is fixed and known in advance, computing the universal model is often inefficient as many inferences made during this process can be irrelevant to a given query. In such cases, a goal-driven approach, which avoids drawing unnecessary inferences, promises to be more efficient and thus preferable in practice. In this paper we present what we believe to be the first technique for goal-driven query answering over first- and second-order dependencies with equality reasoning. Our technique transforms the input dependencies so that applying the chase to the output avoids many inferences that are irrelevant to the query. The transformation proceeds in several steps, which comprise the following three novel techniques. First, we present a variant of the singularisation technique by Marnette [60] that is applicable to second-order dependencies and that corrects an incompleteness of a related formulation by ten Cate et al. [74]. Second, we present a relevance analysis technique that can eliminate from the input dependencies that provably do not contribute to query answers. Third, we present a variant of the magic sets algorithm [19] that can handle second-order dependencies with equality reasoning. We also present the results of an extensive empirical evaluation, which show that goal-driven query answering can be orders of magnitude faster than computing the full universal model.

Neural Information Processing Systems http://nips.cc/

The protection of sensitive data becomes more vital, as data increases in value and potency. Furthermore, the pressure increases from regulators and society on model developers to make their Artificial Intelligence (AI) models non-discriminatory. To boot, there is a need for interpretable, transparent AI models for high-stakes tasks. In general, measuring the fairness of any AI model requires the sensitive attributes of the individuals in the dataset, thus raising privacy concerns. In this work, the trade-offs between fairness, privacy and interpretability are further explored. We specifically examine the Statistical Parity (SP) of Decision Trees (DTs) with Differential Privacy (DP), that are each popular methods in their respective subfield. We propose a novel method, dubbed Privacy-Aware Fairness Estimation of Rules (PAFER), that can estimate SP in a DP-aware manner for DTs. DP, making use of a third-party legal entity that securely holds this sensitive data, guarantees privacy by adding noise to the sensitive data. We experimentally compare several DP mechanisms. We show that using the Laplacian mechanism, the method is able to estimate SP with low error while guaranteeing the privacy of the individuals in the dataset with high certainty. We further show experimentally and theoretically that the method performs better for DTs that humans generally find easier to interpret.

Variational Information Pursuit (V-IP) is a framework for making interpretable predictions by design by sequentially selecting a short chain of task-relevant, userdefined and interpretable queries about the data that are most informative for the task. While using queries related with semantic concepts allows for built-in interpretability in predictive models, applying V-IP to any task requires data samples with concept-labeling by domain experts, limiting the application of V-IP to smallscale tasks where manual data annotation is feasible. In this work, we extend the V-IP framework with Foundational Models (FMs) to address this limitation. More specifically, we use a two-step process, by first leveraging Large Language Models (LLMs) to generate a sufficiently large candidate set of task-relevant interpretable concepts, then using multimodal models to annotate each data sample by semantic similarity with each concept in the generated concept set. While other interpretableby-design frameworks such as Concept Bottleneck Models (CBMs) require an additional step of removing repetitive and non-discriminative concepts to have good interpretability and test performance, we mathematically and empirically justify that, with a sufficiently informative and task-relevant query (concept) set, the proposed FM+V-IP method does not require any type of concept filtering. In addition, we show that FM+V-IP with LLM generated concepts can achieve better test performance than V-IP with human annotated concepts, demonstrating the effectiveness of LLMs at generating efficient query sets. Finally, when compared to other interpretable-by-design frameworks such as CBMs, FM+V-IP can achieve competitive test performance using fewer number of concepts/queries in both cases with filtered or unfiltered concept sets.

In the digital age, data is a valuable commodity, and data marketplaces offer lucrative opportunities for data owners to monetize their private data. However, data privacy is a significant concern, and differential privacy has become a popular solution to address this issue. Private data trading systems (PDQS) facilitate the trade of private data by determining which data owners to purchase data from, the amount of privacy purchased, and providing specific aggregation statistics while protecting the privacy of data owners. However, existing PDQS with separated procurement and query processes are prone to over-perturbation of private data and lack trustworthiness. To address this issue, this paper proposes a framework for PDQS with an integrated procurement and query process to avoid excessive perturbation of private data. We also present two instances of this framework, one based on a greedy approach and another based on a neural network. Our experimental results show that both of our mechanisms outperformed the separately conducted procurement and query mechanism under the same budget regarding accuracy.