arXiv subjects

Jesse Davis

Publications and source records attributed to Jesse Davis.

47 records · Page 3Linked to original sources

arXiv2017

Induction of Interpretable Possibilistic Logic Theories from Relational Data

The field of Statistical Relational Learning (SRL) is concerned with learning probabilistic models from relational data. Learned SRL models are typically represented using some kind of weighted logical formulas, which make them considerably more interpretable than those obtained by e.g. neural networks. In practice, however, these models are often still difficult to interpret correctly, as they can contain many formulas that interact in non-trivial ways and weights do not always have an intuitive meaning. To address this, we propose a new SRL method which uses possibilistic logic to encode relational models. Learned models are then essentially stratified classical theories, which explicitly encode what can be derived with a given level of certainty. Compared to Markov Logic Networks (MLNs), our method is faster and produces considerably more interpretable models.

cs.AI↗

arXiv2016

Measuring Adverse Drug Effects on Multimorbity using Tractable Bayesian Networks

Managing patients with multimorbidity often results in polypharmacy: the prescription of multiple drugs. However, the long-term effects of specific combinations of drugs and diseases are typically unknown. In particular, drugs prescribed for one condition may result in adverse effects for the other. To investigate which types of drugs may affect the further progression of multimorbidity, we query models of diseases and prescriptions that are learned from primary care data. State-of-the-art tractable Bayesian network representations, on which such complex queries can be computed efficiently, are employed for these large medical networks. Our results confirm that prescriptions may lead to unintended negative consequences in further development of multimorbidity in cardiovascular diseases. Moreover, a drug treatment for one disease group may affect diseases of another group.

cs.AI↗

arXiv2016

Stratified Knowledge Bases as Interpretable Probabilistic Models (Extended Abstract)

In this paper, we advocate the use of stratified logical theories for representing probabilistic models. We argue that such encodings can be more interpretable than those obtained in existing frameworks such as Markov logic networks. Among others, this allows for the use of domain experts to improve learned models by directly removing, adding, or modifying logical formulas.

cs.AI↗

arXiv2016

Learning Possibilistic Logic Theories from Default Rules

We introduce a setting for learning possibilistic logic theories from defaults of the form "if alpha then typically beta". We first analyse this problem from the point of view of machine learning theory, determining the VC dimension of possibilistic stratifications as well as the complexity of the associated learning problems, after which we present a heuristic learning algorithm that can easily scale to thousands of defaults. An important property of our approach is that it is inherently able to handle noisy and conflicting sets of defaults. Among others, this allows us to learn possibilistic logic theories from crowdsourced data and to approximate propositional Markov logic networks using heuristic MAP solvers. We present experimental results that demonstrate the effectiveness of this approach.

cs.AI↗

arXiv2015

Assessing binary classifiers using only positive and unlabeled data

Assessing the performance of a learned model is a crucial part of machine learning. However, in some domains only positive and unlabeled examples are available, which prohibits the use of most standard evaluation metrics. We propose an approach to estimate any metric based on contingency tables, including ROC and PR curves, using only positive and unlabeled data. Estimating these performance metrics is essentially reduced to estimating the fraction of (latent) positives in the unlabeled set, assuming known positives are a random sample of all positives. We provide theoretical bounds on the quality of our estimates, illustrate the importance of estimating the fraction of positives in the unlabeled set and demonstrate empirically that we are able to reliably estimate ROC and PR curves on real data.

stat.ML↗

arXiv2015

Encoding Markov Logic Networks in Possibilistic Logic

Markov logic uses weighted formulas to compactly encode a probability distribution over possible worlds. Despite the use of logical formulas, Markov logic networks (MLNs) can be difficult to interpret, due to the often counter-intuitive meaning of their weights. To address this issue, we propose a method to construct a possibilistic logic theory that exactly captures what can be derived from a given MLN using maximum a posteriori (MAP) inference. Unfortunately, the size of this theory is exponential in general. We therefore also propose two methods which can derive compact theories that still capture MAP inference, but only for specific types of evidence. These theories can be used, among others, to make explicit the hidden assumptions underlying an MLN or to explain the predictions it makes.

cs.AI↗

arXiv2014

Lifted Variable Elimination: Decoupling the Operators from the Constraint Language

Lifted probabilistic inference algorithms exploit regularities in the structure of graphical models to perform inference more efficiently. More specifically, they identify groups of interchangeable variables and perform inference once per group, as opposed to once per variable. The groups are defined by means of constraints, so the flexibility of the grouping is determined by the expressivity of the constraint language. Existing approaches for exact lifted inference use specific languages for (in)equality constraints, which often have limited expressivity. In this article, we decouple lifted inference from the constraint language. We define operators for lifted inference in terms of relational algebra operators, so that they operate on the semantic level (the constraints extension) rather than on the syntactic level, making them language-independent. As a result, lifted inference can be performed using more powerful constraint languages, which provide more opportunities for lifting. We empirically demonstrate that this can improve inference efficiency by orders of magnitude, allowing exact inference where until now only approximate inference was feasible.

cs.AI↗

arXiv2013

First-Order Decomposition Trees

Lifting attempts to speed up probabilistic inference by exploiting symmetries in the model. Exact lifted inference methods, like their propositional counterparts, work by recursively decomposing the model and the problem. In the propositional case, there exist formal structures, such as decomposition trees (dtrees), that represent such a decomposition and allow us to determine the complexity of inference a priori. However, there is currently no equivalent structure nor analogous complexity results for lifted inference. In this paper, we introduce FO-dtrees, which upgrade propositional dtrees to the first-order level. We show how these trees can characterize a lifted inference solution for a probabilistic logical model (in terms of a sequence of lifted operations), and make a theoretical analysis of the complexity of lifted inference in terms of the novel notion of lifted width for the tree.

cs.AI↗

arXiv2012

Lifted Variable Elimination: A Novel Operator and Completeness Results

Various methods for lifted probabilistic inference have been proposed, but our understanding of these methods and the relationships between them is still limited, compared to their propositional counterparts. The only existing theoretical characterization of lifting is for weighted first-order model counting (WFOMC), which was shown to be complete domain-lifted for the class of 2-logvar models. This paper makes two contributions to lifted variable elimination (LVE). First, we introduce a novel inference operator called group inversion. Second, we prove that LVE augmented with this operator is complete in the same sense as WFOMC.

cs.AI↗

arXiv2012

Unachievable Region in Precision-Recall Space and Its Effect on Empirical Evaluation

Precision-recall (PR) curves and the areas under them are widely used to summarize machine learning results, especially for data sets exhibiting class skew. They are often used analogously to ROC curves and the area under ROC curves. It is known that PR curves vary as class skew changes. What was not recognized before this paper is that there is a region of PR space that is completely unachievable, and the size of this region depends only on the skew. This paper precisely characterizes the size of that region and discusses its implications for empirical evaluation methodology in machine learning.

cs.LG↗

arXiv2012

Demand-Driven Clustering in Relational Domains for Predicting Adverse Drug Events

Learning from electronic medical records (EMR) is challenging due to their relational nature and the uncertain dependence between a patient's past and future health status. Statistical relational learning is a natural fit for analyzing EMRs but is less adept at handling their inherent latent structure, such as connections between related medications or diseases. One way to capture the latent structure is via a relational clustering of objects. We propose a novel approach that, instead of pre-clustering the objects, performs a demand-driven clustering during learning. We evaluate our algorithm on three real-world tasks where the goal is to use EMRs to predict whether a patient will have an adverse reaction to a medication. We find that our approach is more accurate than performing no clustering, pre-clustering, and using expert-constructed medical heterarchies.

cs.LG↗