Explanatory Interactive Learning (XIL) is a powerful interactive learning framework designed to enable users to customize and correct AI models by interacting with their explanations. In a nutshell, XIL algorithms select a number of items on which an AI model made a decision (e.g., images and their tags) and present them to users, together with corresponding explanations (e.g., image regions that drive the model’s decision). Then, users supply corrective feedback for the explanations, which the algorithm uses to improve the model. Despite showing promise in debugging tasks, recent studies have raised concerns that explanatory interaction may trigger order effects, a well-known cognitive bias in which the sequence of presented items influences users’ trust and, critically, the quality of their feedback. We argue that these studies are not entirely conclusive, as the experimental designs and tasks employed differ substantially from common XIL use cases, complicating interpretation. To clarify the interplay between order effects and explanatory interaction, we ran a larger-scale user study (n = 713 total) designed to mimic common XIL tasks. Specifically, we assessed order effects both within and between debugging sessions by manipulating the order in which correct and wrong explanations are presented to participants. Order effects had a limited but significant impact on users’ agreement with the model (i.e., a behavioral measure of their trust), and only when examined within debugging sessions, not between them. The quality of users’ feedback reached satisfactory levels overall, with order effects exerting only a small and inconsistent influence both within and between sessions. Overall, our findings suggest that order effects do not pose a significant issue to the successful employment of XIL approaches. More broadly, our work contributes to the ongoing efforts for understanding human factors in AI.

Abstract Concept Bottleneck Models (CBMs) are neural networks designed to conjoin high performance with ante-hoc interpretability. CBMs work by first mapping inputs (e.g., images) to high-level concepts (e.g., visible objects and their properties) and then use these to solve a downstream task (e.g., tagging or scoring an image) in an interpretable manner. Their performance and interpretability, however, hinge on the quality of the concepts they learn . The go-to strategy for ensuring good quality concepts is to leverage expert annotations, which are expensive to collect and seldom available in applications. Researchers have recently addressed this issue by introducing “VLM-CBM” architectures that replace manual annotations with weak supervision from foundation models. It is however unclear what the impact of doing so is on the quality of the learned concepts. To answer this question, we put state-of-the-art VLM-CBMs to the test, analyzing their learned concepts empirically using a selection of significant metrics. Our results show that, depending on the task, VLM supervision can noticeably differ from expert annotations, and that concept accuracy and quality are not strongly correlated. Our code is available at https://github.com/debryu/CQA .

As Graph Neural Networks (GNNs) become more pervasive, it becomes paramount to build reliable tools for explaining their predictions. A core desideratum is that explanations are *faithful*, i.e., that they portray an accurate picture of the GNN's reasoning process. However, a number of different faithfulness metrics exist, begging the question of what is faithfulness exactly and how to achieve it. We make three key contributions. We begin by showing that *existing metrics are not interchangeable* -- i.e., explanations attaining high faithfulness according to one metric may be unfaithful according to others -- and can *systematically ignore important properties of explanations*. We proceed to show that, surprisingly, *optimizing for faithfulness is not always a sensible design goal*. Specifically, we prove that for injective regular GNN architectures, perfectly faithful explanations are completely uninformative. This does not apply to modular GNNs, such as self-explainable and domain-invariant architectures, prompting us to study the relationship between architectural choices and faithfulness. Finally, we show that *faithfulness is tightly linked to out-of-distribution generalization*, in that simply ensuring that a GNN can correctly recognize the domain-invariant subgraph, as prescribed by the literature, does not guarantee that it is invariant unless this subgraph is also faithful. All our code can be found in the supplementary material.

Current large language models (LLMs) are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict themselves when prompted to reason about relations between real entities of the world. These problems are currently addressed with large scale fine-tuning or by delegating consistent reasoning to external tools. In this work, we strive for a middle ground and leverage a training objective based on a principled neuro-symbolic loss that teaches a LLM to be consistent with external knowledge in the form of a set of facts and rules. Fine-tuning with such a loss on a limited set of facts enables our LLMs to be more logically consistent than previous baselines for a given constraint. Our approach also allows to easily combine multiple logical constraints at once in a principled way, delivering LLMs that are more consistent w.r.t. all the selected rules. Moreover, our method allows LLMs to extrapolate to unseen but semantically similar factual knowledge, represented in unseen datasets, more systematically.

Self-Explainable Graph Neural Networks (SE-GNNs) are popular explainable-by-design GNNs, but their explanations' properties and limitations are not well understood. Our first contribution fills this gap by formalizing the explanations extracted by some popular SE-GNNs, referred to as Minimal Explanations (MEs), and comparing them to established notions of explanations, namely Prime Implicant (PI) and faithful explanations. Our analysis reveals that MEs match PI explanations for a restricted but significant family of tasks. In general, however, they can be less informative than PI explanations and are surprisingly misaligned with widely accepted notions of faithfulness. Although faithful and PI explanations are informative, they are intractable to find and we show that they can be prohibitively large. Given these observations, a natural choice is to augment SE-GNNs with alternative modalities of explanations taking care of SE-GNNs’ limitations. To this end, we propose Dual-Channel GNNs that integrate a white-box rule extractor and a standard SE-GNN, adaptively combining both channels. Our experiments show that even a simple instantiation of Dual-Channel GNNs can recover succinct rules and perform on par or better than widely used SE-GNNs.

Concept-based Models are neural networks that learn a concept extractor to map inputs to high-level concepts and an inference layer to translate these into predictions. Ensuring these modules produce interpretable concepts and behave reliably in out-of-distribution is crucial, yet the conditions for achieving this remain unclear. We study this problem by establishing a novel connection between Concept-based Models and reasoning shortcuts (RSs), a common issue where models achieve high accuracy by learning low-quality concepts, even when the inference layer is fixed and provided upfront. Specifically, we extend RSs to the more complex setting of Concept-based Models and derive theoretical conditions for identifying both the concepts and the inference layer. Our empirical results highlight the impact of RSs and show that existing methods, even combined with multiple natural mitigation strategies, often fail to meet these conditions in practice.

The advent of powerful neural classifiers has increased interest in problems that require both learning and reasoning.These problems are critical for understanding important properties of models, such as trustworthiness, generalization, interpretability, and compliance to safety and structural constraints. However, recent research observed that tasks requiring both learning and reasoning on background knowledge often suffer from reasoning shortcuts (RSs): predictors can solve the downstream reasoning task without associating the correct concepts to the high-dimensional data. To address this issue, we introduce rsbench, a comprehensive benchmark suite designed to systematically evaluate the impact of RSs on models by providing easy access to highly customizable tasks affected by RSs. Furthermore, rsbench implements common metrics for evaluating concept quality and introduces novel formal verification procedures for assessing the presence of RSs in learning tasks. Using rsbench, we highlight that obtaining high quality concepts in both purely neural and neuro-symbolic models is a far-from-solved problem. rsbench is available at: https://unitn-sml.github.io/rsbench.

Neuro-Symbolic (NeSy) predictors that conform to symbolic knowledge {–} encoding, e.g., safety constraints {–} can be affected by Reasoning Shortcuts (RSs): They learn concepts consistent with the symbolic knowledge by exploiting unintended semantics. RSs compromise reliability and generalization and, as we show in this paper, they are linked to NeSy models being overconfident about the predicted concepts. Unfortunately, the only trustworthy mitigation strategy requires collecting costly dense supervision over the concepts. Rather than attempting to avoid RSs altogether, we propose to ensure NeSy models are aware of the semantic ambiguity of the concepts they learn, thus enabling their users to identify and distrust low-quality concepts. Starting from three simple desiderata, we derive bears (BE Aware of Reasoning Shortcuts), an ensembling technique that calibrates the model’s concept-level confidence without compromising prediction accuracy, thus encouraging NeSy architectures to be uncertain about concepts affected by RSs. We show empirically that bears improves RS-awareness of several state-of-the-art NeSy models, and also facilitates acquiring informative dense annotations for mitigation purposes.

We introduce Neuro-Symbolic Continual Learning, where a model has to solve a sequence of neuro-symbolic tasks, that is, it has to map sub-symbolic inputs to high-level concepts and compute predictions by reasoning consistently with prior knowledge. Our key observation is that neuro-symbolic tasks, although different, often share concepts whose semantics remains stable over time. Traditional approaches fall short: existing continual strategies ignore knowledge altogether, while stock neuro-symbolic architectures suffer from catastrophic forgetting. We show that leveraging prior knowledge by combining neuro-symbolic architectures with continual strategies does help avoid catastrophic forgetting, but also that doing so can yield models affected by reasoning shortcuts. These undermine the semantics of the acquired concepts, even when detailed prior knowledge is provided upfront and inference is exact, and in turn continual performance. To overcome these issues, we introduce COOL, a COncept-level cOntinual Learning strategy tailored for neuro-symbolic continual problems that acquires high-quality concepts and remembers them over time. Our experiments on three novel benchmarks highlights how COOL attains sustained high performance on neuro-symbolic continual learning tasks in which other strategies fail.

Neuro-Symbolic (NeSy) predictive models hold the promise of improved compliance with given constraints, systematic generalization, and interpretability, as they allow to infer labels that are consistent with some prior knowledge by reasoning over high-level concepts extracted from sub-symbolic inputs. It was recently shown that NeSy predictors are affected by *reasoning shortcuts*: they can attain high accuracy but by leveraging concepts with \textit{unintended semantics}, thus coming short of their promised advantages. Yet, a systematic characterization of reasoning shortcuts and of potential mitigation strategies is missing. This work fills this gap by characterizing them as unintended optima of the learning objective and identifying four key conditions behind their occurrence. Based on this, we derive several natural mitigation strategies, and analyze their efficacy both theoretically and empirically. Our analysis shows reasoning shortcuts are difficult to deal with, casting doubts on the trustworthiness and interpretability of existing NeSy solutions.

Automated persuasion systems (APS) aim to persuade a user to believe something by entering into a dialogue in which arguments and counterarguments are exchanged. To maximize the probability that an APS is successful in persuading a user, it can identify a global policy that will allow it to select the best arguments it presents at each stage of the dialogue whatever arguments the user presents. However, in real applications, such as for healthcare, it is unlikely the utility of the outcome of the dialogue will be the same, or the exact opposite, for the APS and user. In order to deal with this situation, games in extended form have been harnessed for argumentation in Bi-party Decision Theory. This opens new problems that we address in this paper: (1) How can we use Machine Learning (ML) methods to predict utility functions for different subpopulations of users? and (2) How can we identify for a new user the best utility function from amongst those that we have learned. To this extent, we develop two ML methods, EAI and EDS, that leverage information coming from the users to predict their utilities. EAI is restricted to a fixed amount of information, whereas EDS can choose the information that best detects the subpopulations of a user. We evaluate EAI and EDS in a simulation setting and in a realistic case study concerning healthy eating habits. Results are promising in both cases, but EDS is more effective at predicting useful utility functions.

Federated Learning (FL) is an emerging privacy-aware machine learning technique that applies successfully to the collaborative learning of global models for Human Activity Recognition (HAR). As of now, the applications of FL for HAR assume that the data associated with diverse individuals follow the same distribution. However, this assumption is impractical in real-world scenarios where the same activity is frequently performed differently by different individuals. To tackle this issue, we propose FedMAT, a Federated Multi-task ATtention framework for HAR, which extracts and fuses shared as well as individual-specific multi-modal sensor data features. Specifically, we treat the HAR problem associated with each individual as a different task and train a federated multi-task model, composed of a shared feature representation network in a central server plus multiple individual-specific networks with attention modules stored in decentralized nodes. In this architecture, the attention module operates as a mask that allows to learn individual-specific features from the global model, whilst simultaneously allowing for features to be shared among different individuals. We conduct extensive experiments based on publicly available HAR datasets, which are collected in both controlled environments and real-world scenarios. Numeric results verify that our proposed FedMAT significantly outperforms baselines not only in generalizing to existing individuals but also in adapting to new individuals.

We design a predictive layer for structured-output prediction (SOP) that can be plugged into any neural network guaranteeing its predictions are consistent with a set of predefined symbolic constraints. Our Semantic Probabilistic Layer (SPL) can model intricate correlations, and hard constraints, over a structured output space all while being amenable to end-to-end learning via maximum likelihood.SPLs combine exact probabilistic inference with logical reasoning in a clean and modular way, learning complex distributions and restricting their support to solutions of the constraint. As such, they can faithfully, and efficiently, model complex SOP tasks beyond the reach of alternative neuro-symbolic approaches. We empirically demonstrate that SPLs outperform these competitors in terms of accuracy on challenging SOP tasks such as hierarchical multi-label classification, pathfinding and preference learning, while retaining perfect constraint satisfaction.

There is growing interest in concept-based models (CBMs) that combine high-performance and interpretability by acquiring and reasoning with a vocabulary of high-level concepts. A key requirement is that the concepts be interpretable. Existing CBMs tackle this desideratum using a variety of heuristics based on unclear notions of interpretability, and fail to acquire concepts with the intended semantics. We address this by providing a clear definition of interpretability in terms of alignment between the model’s representation and an underlying data generation process, and introduce GlanceNets, a new CBM that exploits techniques from disentangled representation learning and open-set recognition to achieve alignment, thus improving the interpretability of the learned concepts. We show that GlanceNets, paired with concept-level supervision, achieve better alignment than state-of-the-art approaches while preventing spurious information from unintendedly leaking into the learned concepts.

Abstract We introduce and study knowledge drift (KD), a special form of concept drift that occurs in hierarchical classification. Under KD the vocabulary of concepts, their individual distributions, and the is-a relations between them can all change over time. The main challenge is that, since the ground-truth concept hierarchy is unobserved, it is hard to tell apart different forms of KD. For instance, the introduction of a new is-a relation between two concepts might be confused with changes to those individual concepts, but it is far from equivalent. Failure to identify the right kind of KD compromises the concept hierarchy used by the classifier, leading to systematic prediction errors. Our key observation is that in human-in-the-loop applications like smart personal assistants the user knows what kind of drift occurred recently, if any. Motivated by this observation, we introduce trckd, a novel approach that combines two automated stages—drift detection and adaptation—with a new interactive disambiguation stage in which the user is asked to refine the machine’s understanding of recently detected KD. In addition, trckd implements a simple but effective knowledge-aware adaptation strategy. Our simulations show that, when the structure of the concept hierarchy drifts, a handful of queries to the user are often enough to substantially improve prediction performance on both synthetic and realistic data.

We tackle sequential learning under label noise in applications where a human supervisor can be queried to relabel suspicious examples. Existing approaches are flawed, in that they only relabel incoming examples that look "suspicious" to the model. As a consequence, those mislabeled examples that elude (or don't undergo) this cleaning step end up tainting the training data and the model with no further chance of being cleaned. We propose CINCER, a novel approach that cleans both new and past data by identifying \emph{pairs of mutually incompatible examples}. Whenever it detects a suspicious example, CINCER identifies a counter-example in the training set that - according to the model - is maximally incompatible with the suspicious example, and asks the annotator to relabel either or both examples, resolving this possible inconsistency. The counter-examples are chosen to be maximally incompatible, so to serve as \emph{explanations} of the model's suspicion, and highly influential, so to convey as much information as possible if relabeled. CINCER achieves this by leveraging an efficient and robust approximation of influence functions based on the Fisher information matrix (FIM). Our extensive empirical evaluation shows that clarifying the reasons behind the model's suspicions by cleaning the counter-examples helps in acquiring substantially better data and models, especially when paired with our FIM approximation.

Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine learning---from computing the expectations of decision tree ensembles to information-theoretic divergences of sum-product networks---can be represented in terms of tractable modular operations over circuits. Specifically, we characterize the tractability of simple transformations---sums, products, quotients, powers, logarithms, and exponentials---in terms of sufficient structural constraints of the circuits they operate on, and present novel hardness results for the cases in which these properties are not satisfied. Building on these operations, we derive a unified framework for reasoning about tractable models that generalizes several results in the literature and opens up novel tractable inference scenarios.

Combinatorial optimization problems are ubiquitous in artificial intelligence. Designing the underlying models, however, requires substantial expertise, which is a limiting factor in practice. The models typically consist of hard and soft constraints, or combine hard constraints with a preference function. We introduce a novel setting for learning combinatorial optimisation problems from contextual examples. These positive and negative examples show – in a particular context – whether the solutions are good enough or not. We develop our framework using the MAX-SAT formalism. We provide learnability results within the realizable and agnostic settings, as well as hassle, an implementation based on syntax-guided synthesis and showcase its promise on recovering synthetic and benchmark instances from examples.

Weighted model integration (WMI) is a framework for probabilistic inference over distributions with discrete and continuous variables and structured supports. Despite the growing popularity of WMI, existing density estimators ignore the problem of learning a structured support, and thus fail to handle unfeasible configurations and piecewise-linear relations between continuous variables. We propose lariat, a novel method to tackle this challenging problem. In a first step, our approach induces an SMT(ℒℛA) formula representing the support of the structured distribution. Next, it combines the latter with a density learned using a state-of-the-art estimation method. The overall model automatically accounts for the discontinuous nature of the underlying structured distribution. Our experimental results with synthetic and real-world data highlight the promise of the approach.

The ability to learn from human supervision is fundamental for personal assistants and other interactive applications of AI. Two central challenges for deploying interactive learners in the wild are the unreliable nature of the supervision and the varying complexity of the prediction task. We address a simple but representative setting, incremental classification in the wild, where the supervision is noisy and the number of classes grows over time. In order to tackle this task, we propose a redesign of skeptical learning centered around Gaussian Processes (GPs). Skeptical learning is a recent interactive strategy in which, if the machine is sufficiently confident that an example is mislabeled, it asks the annotator to reconsider her feedback. In many cases, this is often enough to obtain clean supervision. Our redesign, dubbed ISGP , leverages the uncertainty estimates supplied by GPs to better allocate labeling and contradiction queries, especially in the presence of noise. Our experiments on synthetic and real-world data show that, as a result, while the original formulation of skeptical learning produces over-confident models that can fail completely in the wild, ISGP works well at varying levels of noise and as new classes are observed.

Generative Adversarial Networks (GANs) struggle to generate structured objects like molecules and game maps. The issue is that structured objects must satisfy hard requirements (e.g., molecules must be chemically valid) that are difficult to acquire from examples alone. As a remedy, we propose Constrained Adversarial Networks (CANs), an extension of GANs in which the constraints are embedded into the model during training. This is achieved by penalizing the generator proportionally to the mass it allocates to invalid structures. In contrast to other generative models, CANs support efficient inference of valid structures (with high probability) and allows to turn on and off the learned constraints at inference time. CANs handle arbitrary logical constraints and leverage knowledge compilation techniques to efficiently evaluate the disagreement between the model and the constraints. Our setup is further extended to hybrid logical-neural constraints for capturing very complex constraints, like graph reachability. An extensive empirical analysis shows that CANs efficiently generate valid structures that are both high-quality and novel.

Although interactive learning puts the user into the loop, the learner remains mostly a black box for the user. Understanding the reasons behind predictions and queries is important when assessing how the learner works and, in turn, trust. Consequently, we propose the novel framework of explanatory interactive learning where, in each step, the learner explains its query to the user, and the user interacts by both answering the query and correcting the explanation. We demonstrate that this can boost the predictive and explanatory powers of, and the trust into, the learned model, using text (e.g. SVMs) and image classification (e.g. neural networks) experiments as well as a user study.

Many problems in operations research require that constraints be specified in the model. Determining right constraints is a hard and laborsome task. We propose an approach to automate this process using artificial intelligence and machine learning principles. We focus on personnel rostering and scheduling problems in which there are often past schedules available and show that it is possible to automatically learn constraints from such examples. To realize this, we adapted some techniques from the constraint programming community and extended them in order to cope with multidimensional examples. The method uses a tensor representation of the example, which helps in capturing the dimensionality as well as the structure of the example, and applies tensor operations to find the constraints that are satisfied by the example. The algorithm also identifies inherent clusters in the data and uses it as background knowledge to learn more detailed constraints. To evaluate the proposed algorithm, we used constraints from the Nurse Rostering Competition and generated solutions that satisfy these constraints; these solutions were then used as examples to learn constraints. Experiments demonstrate that the proposed algorithm is capable of producing human readable constraints that capture the underlying characteristics of the examples.

Linear Programming lies at the core of mathematical modelling and optimization. Designing linear programs (LPs) is a difficult and expensive process, as it requires both mathematical programming and domain expertise, and it involves both designing an objective function and feasibility constraints. To support this design process, we propose INCALP, an algorithm for inducing linear programs from examples. Since the objective can often be learned with standard techniques (e.g. regression), INCALP learns the hard constraints only. It does so by encoding constraint learning as a mixed integer linear program. INCALP achieves significant efficiency gains by considering gradually larger subsets of examples, and terminating as soon as a suitable program is found. In addition, INCALP encourages both compactness and sparsity of the learned program. Our empirical analysis on synthetic data and textbook problems highlights the promise of the approach.

Integer programming (IP) is widely used within operations research to model and solve complex combinatorial problems such as personnel rostering and assignment problems. Modelling such problems is difficult for non-experts and expensive when hiring domain experts to perform the modelling. For many tasks, however, examples of working solutions are readily available. We propose ARNOLD, an approach that partially automates the modelling step by learning an integer program from example solutions. Contrary to existing alternatives, ARNOLD natively handles multi-dimensional quantities and non-linear operations, which are at the core of IP problems, and it only requires examples of feasible solution. The main challenge is to efficiently explore the space of possible programs. Our approach pairs a general-to-specific traversal strategy with a nested lexicographic ordering in order to prune large portions of the space of candidate constraints while avoiding visiting the same candidate multiple times. Our empirical evaluation shows that ARNOLD can acquire models for a number of realistic benchmark problems

BACKGROUND: The advent of high-throughput experimental techniques paved the way to genome-wide computational analysis and predictive annotation studies. When considering the joint annotation of a large set of related entities, like all proteins of a certain genome, many candidate annotations could be inconsistent, or very unlikely, given the existing knowledge. A sound predictive framework capable of accounting for this type of constraints in making predictions could substantially contribute to the quality of machine-generated annotations at a genomic scale. RESULTS: We present OCELOT, a predictive pipeline which simultaneously addresses functional and interaction annotation of all proteins of a given genome. The system combines sequence-based predictors for functional and protein-protein interaction (PPI) prediction with a consistency layer enforcing (soft) constraints as fuzzy logic rules. The enforced rules represent the available prior knowledge about the classification task, including taxonomic constraints over each GO hierarchy (e.g. a protein labeled with a GO term should also be labeled with all ancestor terms) as well as rules combining interaction and function prediction. An extensive experimental evaluation on the Yeast genome shows that the integration of prior knowledge via rules substantially improves the quality of the predictions. The system largely outperforms GoFDR, the only high-ranking system at the last CAFA challenge with a readily available implementation, when GoFDR is given access to intra-genome information only (as OCELOT), and has comparable or better results (depending on the hierarchy and performance measure) when GoFDR is allowed to use information from other genomes. Our system also compares favorably to recent methods based on deep learning.

We tackle the problem of constructive preference elicitation, that is the problem of learning user preferences over verylarge decision problems, involving a combinatorial space of possible outcomes. In this setting, the suggested configuration is synthesized on-the-fly by solving a constrained optimization problem, while the preferences are learned iteratively by interacting with the user. Previous work has shown that Coactive Learning is a suitable method for learning userpreferences in constructive scenarios. In Coactive Learning the user provides feedback to the algorithm in the form of an improvement to a suggested configuration. When the problem involves many decision variables and constraints, this type of interaction poses a significant cognitive burden on the user. We propose a decomposition technique for large preference-based decision problems relying exclusively on inference and feedback over partial configurations. This has the clear advantage of drastically reducing the user cognitive load. Additionally, part-wise inference can be (up to exponentially) less computationally demanding than inference over full configurations. We discuss the theoretical implications of working with parts and present promising empirical results on one synthetic and two realistic constructive problems.

Peference elicitation is the task of suggesting a highly preferred configuration to a decision maker. The preferences are typically learned by querying the user for choice feedback over pairs or sets of objects. In its constructive variant, new objects are synthesized "from scratch" by maximizing an estimate of the user utility over a combinatorial (possibly infinite) space of candidates. In the constructive setting, most existing elicitation techniques fail because they rely on exhaustive enumeration of the candidates. A previous solution explicitly designed for constructive tasks comes with no formal performance guarantees, and can be very expensive in (or unapplicable to) problems with non-Boolean attributes. We propose the Choice Perceptron, a Perceptron-like algorithm for learning user preferences from set-wise choice feedback over constructive domains and hybrid Boolean-numeric feature spaces. We provide a theoretical analysis on the attained regret that holds for a large class of query selection strategies, and devise a heuristic strategy that aims at optimizing the regret in practice. Finally, we demonstrate its effectiveness by empirical evaluation against existing competitors on constructive scenarios of increasing complexity.

While constraints are ubiquitous in artificial intelligence and constraints are also commonly used in machine learning and data mining, the problem of learning constraints from examples has received less attention. In this paper, we discuss the problem of constraint learning in detail, indicate some subtle differences with standard machine learning problems, sketch some applications and summarize the state-of-the-art.

Constructive learning is the task of learning to synthesize structured objects from data. Examples range from classical sequence labeling to layout synthesis and drug design. Learning in these scenarios involves repeatedly synthesizing candidates subject to feasibility constraints and adapting the model based on the observed loss. Many synthesis problems of interest are non-standard: they involve discrete and continuous variables as well as arbitrary constraints among them. In these cases, widespread formalisms (like linear programming) can not be applied, and the developer is left with writing her own ad-hoc solver. This can be very time consuming and error prone. We introduce Pyconstruct, a Python library tailored for solving real-world constructive problems with minimal effort. The library leverages max-margin approaches to decouple learning from synthesis and constraint programming as a generic framework for synthesis. Pyconstruct enables easy prototyping of working solutions, allowing developers to write complex synthesis problems in a declarative fashion in few lines of code. The library is available at: http://bit.ly/2st8nt3

We introduce the problem of learning SMT(LRA) constraints from data. SMT(LRA) extends propositional logic with (in)equalities between numerical variables. Many relevant formal verification problems can be cast as SMT(LRA) instances and SMT(LRA) has supported recent developments in optimization and counting for hybrid Boolean and numerical domains. We introduce SMT(LRA) learning, the task of learning SMT(LRA) formulas from examples of feasible and infeasible instances, and we contribute INCAL, an exact non-greedy algorithm for this setting. Our approach encodes the learning task itself as an SMT(LRA) satisfiability problem that can be solved directly by SMT solvers. INCAL is an incremental algorithm that achieves exact learning by looking only at a small subset of the data, leading to significant speed-ups. We empirically evaluate our approach on both synthetic instances and benchmark problems taken from the SMT-LIB benchmarks repository.

When faced with complex choices, users refine their own preference criteria as they explore the catalogue of options. In this paper we propose an approach to preference elicitation suited for this scenario. We extend Coactive Learning, which iteratively collects manipulative feedback, to optionally query example critiques. User critiques are integrated into the learning model by dynamically extending the feature space. Our formulation natively supports constructive learning tasks, where the option catalogue is generated on-the-fly. We present an upper bound on the average regret suffered bythe learner. Our empirical analysis highlights the promise of our approach.

Background: Viruses are typically characterized by high mutation rates, which allow them to quickly develop drug-resistant mutations. Mining relevant rules from mutation data can be extremely useful to understand the virus adaptation mechanism and to design drugs that e↵ectively counter potentially resistant mutants. Results: We propose a simple relational learning approach for mutant prediction where the input consists of mutation data with drug-resistance information, either as sets of mutations conferring resistance to a certain drug, or as sets of mutants with information on their susceptibility to the drug. The algorithm learns a set of relational rules characterizing drug-resistance and use them to generate a set of potentially resistant mutants. Conclusions: Promising results were obtained in generating resistant mutations for both nucleoside and nonnucleoside HIV reverse transcriptase inhibitors. The approach can be generalized quite easily to learning mutants characterized by more complex rules correlating multiple mutations. Background HIV is a pandemic cause of lethal pathologies in more than 33 million people. Its horizontal transmission trough mucosae is di cult to control and treat

BACKGROUND: Protein-protein interactions can be seen as a hierarchical process occurring at three related levels: proteins bind by means of specific domains, which in turn form interfaces through patches of residues. Detailed knowledge about which domains and residues are involved in a given interaction has extensive applications to biology, including better understanding of the binding process and more efficient drug/enzyme design. Alas, most current interaction prediction methods do not identify which parts of a protein actually instantiate an interaction. Furthermore, they also fail to leverage the hierarchical nature of the problem, ignoring otherwise useful information available at the lower levels; when they do, they do not generate predictions that are guaranteed to be consistent between levels. RESULTS: Inspired by earlier ideas of Yip et al. (BMC Bioinformatics 10:241, 2009), in the present paper we view the problem as a multi-level learning task, with one task per level (proteins, domains and residues), and propose a machine learning method that collectively infers the binding state of all object pairs. Our method is based on Semantic Based Regularization (SBR), a flexible and theoretically sound machine learning framework that uses First Order Logic constraints to tie the learning tasks together. We introduce a set of biologically motivated rules that enforce consistent predictions between the hierarchy levels. CONCLUSIONS: We study the empirical performance of our method using a standard validation procedure, and compare its performance against the only other existing multi-level prediction technique. We present results showing that our method substantially outperforms the competitor in several experimental settings, indicating that exploiting the hierarchical nature of the problem can lead to better predictions. In addition, our method is also guaranteed to produce interactions that are consistent with respect to the protein-domain-residue hierarchy.

BACKGROUND: Computational methods for the prediction of protein features from sequence are a long-standing focus of bioinformatics. A key observation is that several protein features are closely inter-related, that is, they are conditioned on each other. Researchers invested a lot of effort into designing predictors that exploit this fact. Most existing methods leverage inter-feature constraints by including known (or predicted) correlated features as inputs to the predictor, thus conditioning the result. RESULTS: By including correlated features as inputs, existing methods only rely on one side of the relation: the output feature is conditioned on the known input features. Here we show how to jointly improve the outputs of multiple correlated predictors by means of a probabilistic-logical consistency layer. The logical layer enforces a set of weighted first-order rules encoding biological constraints between the features, and improves the raw predictions so that they least violate the constraints. In particular, we show how to integrate three stand-alone predictors of correlated features: subcellular localization (Loctree [J Mol Biol 348:85-100, 2005]), disulfide bonding state (Disulfind [Nucleic Acids Res 34:W177-W181, 2006]), and metal bonding state (MetalDetector [Bioinformatics 24:2094-2095, 2008]), in a way that takes into account the respective strengths and weaknesses, and does not require any change to the predictors themselves. We also compare our methodology against two alternative refinement pipelines based on state-of-the-art sequential prediction methods. CONCLUSIONS: The proposed framework is able to improve the performance of the underlying predictors by removing rule violations. We show that different predictors offer complementary advantages, and our method is able to integrate them using non-trivial constraints, generating more consistent predictions. In addition, our framework is fully general, and could in principle be applied to a vast array of heterogeneous predictions without requiring any change to the underlying software. On the other hand, the alternative strategies are more specific and tend to favor one task at the expense of the others, as shown by our experimental evaluation. The ultimate goal of our framework is to seamlessly integrate full prediction suites, such as Distill [BMC Bioinformatics 7:402, 2006] and PredictProtein [Nucleic Acids Res 32:W321-W326, 2004].