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We study the identification of causal effects, motivated by two improvements to identifiability that can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable causal effect may become identifiable when certain variables are functional. Secondly, certain functional variables can be excluded from being observed without affecting the identifiability of a causal effect, which may significantly reduce the number of needed variables in observational data. Our results are largely based on an elimination procedure that removes functional variables from a causal graph while preserving key properties in the resulting causal graph, including the identifiability of causal effects. Our treatment of functional dependencies in this context mandates a formal, systematic, and general treatment of positivity assumptions, which are prevalent in the literature on causal effect identifiability and which interact with functional dependencies, leading to another contribution of the presented work.

Predicting the likelihood of success of weight loss interventions using machine learning (ML) models may enhance intervention effectiveness by enabling timely and dynamic modification of intervention components for nonresponders to treatment. However, a lack of understanding and trust in these ML models impacts adoption among weight management experts. Recent advances in the field of explainable artificial intelligence enable the interpretation of ML models, yet it is unknown whether they enhance model understanding, trust, and adoption among weight management experts. This study aimed to build and evaluate an ML model that can predict 6-month weight loss success (ie, ≥7% weight loss) from 5 engagement and diet-related features collected over the initial 2 weeks of an intervention, to assess whether providing ML-based explanations increases weight management experts’ agreement with ML model predictions, and to inform factors that influence the understanding and trust of ML models to advance explainability in early prediction of weight loss among weight management experts. We trained an ML model using the random forest (RF) algorithm and data from a 6-month weight loss intervention (N=419). We leveraged findings from existing explainability metrics to develop Prime Implicant Maintenance of Outcome (PRIMO), an interactive tool to understand predictions made by the RF model. We asked 14 weight management experts to predict hypothetical participants’ weight loss success before and after using PRIMO. We compared PRIMO with 2 other explainability methods, one based on feature ranking and the other based on conditional probability. We used generalized linear mixed-effects models to evaluate participants’ agreement with ML predictions and conducted likelihood ratio tests to examine the relationship between explainability methods and outcomes for nested models. We conducted guided interviews and thematic analysis to study the impact of our tool on experts’ understanding and trust in the model. Our RF model had 81% accuracy in the early prediction of weight loss success. Weight management experts were significantly more likely to agree with the model when using PRIMO (χ[sup.2]=7.9; P=.02) compared with the other 2 methods with odds ratios of 2.52 (95% CI 0.91-7.69) and 3.95 (95% CI 1.50-11.76). From our study, we inferred that our software not only influenced experts’ understanding and trust but also impacted decision-making. Several themes were identified through interviews: preference for multiple explanation types, need to visualize uncertainty in explanations provided by PRIMO, and need for model performance metrics on similar participant test instances. Our results show the potential for weight management experts to agree with the ML-based early prediction of success in weight loss treatment programs, enabling timely and dynamic modification of intervention components to enhance intervention effectiveness. Our findings provide methods for advancing the understandability and trust of ML models among weight management experts.

Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the decades. The existential quantification of literals (variable states) and its applications have also been studied in the literature. In this paper, we complement this by introducing and studying universal literal quantification and its applications, particularly to explainable AI. We also provide a novel semantics for quantification, discuss the interplay between variable/literal and existential/universal quantification, and identify some classes of Boolean formulas and circuits on which quantification can be done efficiently. Literal quantification is more fine-grained than variable quantification as the latter can be defined in terms of the former, leading to a refinement of quantified Boolean logic with literal quantification as its primitive.

State-of-the-art model counters are based on exhaustive DPLL algorithms, and have been successfully used in probabilistic reasoning, one of the key problems in AI. In this article, we present a new exhaustive DPLL algorithm with a formal semantics, a proof of correctness, and a modular design. The modular design is based on the separation of the core model counting algorithm from SAT solving techniques. We also show that the trace of our algorithm belongs to the language of Sentential Decision Diagrams (SDDs), which is a subset of Decision-DNNFs, the trace of existing state-of-the-art model counters. Still, our experimental analysis shows comparable results against state-of-the-art model counters. Furthermore, we obtain the first top-down SDD compiler, and show orders-of-magnitude improvements in SDD construction time against the existing bottom-up SDD compiler.

We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime. We then provide a knowledge compilation map, which analyzes a large number of existing target compilation languages according to their succinctness and their polytime transformations and queries. We argue that such analysis is necessary for placing new compilation approaches within the context of existing ones. We also go beyond classical, flat target compilation languages based on CNF and DNF, and consider a richer, nested class based on directed acyclic graphs (such as OBDDs), which we show to include a relatively large number of target compilation languages.

When making decisions under uncertainty, the optimal choices are often difficult to discern, especially if not enough information has been gathered. Two key questions in this regard relate to whether one should stop the information gathering process and commit to a decision (stopping criterion), and if not, what information to gather next (selection criterion). In this paper, we show that the recently introduced notion, Same-Decision Probability (SDP), can be useful as both a stopping and a selection criterion, as it can provide additional insight and allow for robust decision making in a variety of scenarios. This query has been shown to be highly intractable, being PP^PP-complete, and is exemplary of a class of queries which correspond to the computation of certain expectations. We propose the first exact algorithm for computing the SDP, and demonstrate its effectiveness on several real and synthetic networks. Finally, we present new complexity results, such as the complexity of computing the SDP on models with a Naive Bayes structure. Additionally, we prove that computing the non-myopic value of information is complete for the same complexity class as computing the SDP.

This paper is concerned with a class of algorithms that perform exhaustive search on propositional knowledge bases. We show that each of these algorithms defines and generates a propositional language. Specifically, we show that the trace of a search can be interpreted as a combinational circuit, and a search algorithm then defines a propositional language consisting of circuits that are generated across all possible executions of the algorithm. In particular, we show that several versions of exhaustive DPLL search correspond to such well-known languages as FBDD, OBDD, and a precisely-defined subset of d-DNNF. By thus mapping search algorithms to propositional languages, we provide a uniform and practical framework in which successful search techniques can be harnessed for compilation of knowledge into various languages of interest, and a new methodology whereby the power and limitations of search algorithms can be understood by looking up the tractability and succinctness of the corresponding propositional languages.

MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation Pr, or the problem of computing the most probable explanation (MPE). This paper investigates the complexity of MAP in Bayesian networks. Specifically, we show that MAP is complete for NP^PP and provide further negative complexity results for algorithms based on variable elimination. We also show that MAP remains hard even when MPE and Pr become easy. For example, we show that MAP is NP-complete when the networks are restricted to polytrees, and even then can not be effectively approximated. Given the difficulty of computing MAP exactly, and the difficulty of approximating MAP while providing useful guarantees on the resulting approximation, we investigate best effort approximations. We introduce a generic MAP approximation framework. We provide two instantiations of the framework; one for networks which are amenable to exact inference Pr, and one for networks for which even exact inference is too hard. This allows MAP approximation on networks that are too complex to even exactly solve the easier problems, Pr and MPE. Experimental results indicate that using these approximation algorithms provides much better solutions than standard techniques, and provide accurate MAP estimates in many cases.