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Fabrizio Riguzzi

Publications and source records attributed to Fabrizio Riguzzi.

28 records · Page 2Linked to original sources

Automatic Setting of DNN Hyper-Parameters by Mixing Bayesian Optimization and Tuning Rules

Deep learning techniques play an increasingly important role in industrial and research environments due to their outstanding results. However, the large number of hyper-parameters to be set may lead to errors if they are set manually. The state-of-the-art hyper-parameters tuning methods are grid search, random search, and Bayesian Optimization. The first two methods are expensive because they try, respectively, all possible combinations and random combinations of hyper-parameters. Bayesian Optimization, instead, builds a surrogate model of the objective function, quantifies the uncertainty in the surrogate using Gaussian Process Regression and uses an acquisition function to decide where to sample the new set of hyper-parameters. This work faces the field of Hyper-Parameters Optimization (HPO). The aim is to improve Bayesian Optimization applied to Deep Neural Networks. For this goal, we build a new algorithm for evaluating and analyzing the results of the network on the training and validation sets and use a set of tuning rules to add new hyper-parameters and/or to reduce the hyper-parameter search space to select a better combination.

cs.LG↗

Quantum Weighted Model Counting

In Weighted Model Counting (WMC) we assign weights to Boolean literals and we want to compute the sum of the weights of the models of a Boolean function where the weight of a model is the product of the weights of its literals. WMC was shown to be particularly effective for performing inference in graphical models, with a complexity of $O(n2^w)$ where $n$ is the number of variables and $w$ is the treewidth. In this paper, we propose a quantum algorithm for performing WMC, Quantum WMC (QWMC), that modifies the quantum model counting algorithm to take into account the weights. In turn, the model counting algorithm uses the algorithms of quantum search, phase estimation and Fourier transform. In the black box model of computation, where we can only query an oracle for evaluating the Boolean function given an assignment, QWMC solves the problem approximately with a complexity of $Θ(2^{\frac{n}{2}})$ oracle calls while classically the best complexity is $Θ(2^n)$, thus achieving a quadratic speedup.

quant-ph↗

Using SWISH to realise interactive web based tutorials for logic based languages

Programming environments have evolved from purely text based to using graphical user interfaces, and now we see a move towards web based interfaces, such as Jupyter. Web based interfaces allow for the creation of interactive documents that consist of text and programs, as well as their output. The output can be rendered using web technology as, e.g., text, tables, charts or graphs. This approach is particularly suitable for capturing data analysis workflows and creating interactive educational material. This article describes SWISH, a web front-end for Prolog that consists of a web server implemented in SWI-Prolog and a client web application written in JavaScript. SWISH provides a web server where multiple users can manipulate and run the same material, and it can be adapted to support Prolog extensions. In this paper we describe the architecture of SWISH, and describe two case studies of extensions of Prolog, namely Probabilistic Logic Programming (PLP) and Logic Production System (LPS), which have used SWISH to provide tutorial sites.

cs.PL↗

Probabilistic DL Reasoning with Pinpointing Formulas: A Prolog-based Approach

When modeling real world domains we have to deal with information that is incomplete or that comes from sources with different trust levels. This motivates the need for managing uncertainty in the Semantic Web. To this purpose, we introduced a probabilistic semantics, named DISPONTE, in order to combine description logics with probability theory. The probability of a query can be then computed from the set of its explanations by building a Binary Decision Diagram (BDD). The set of explanations can be found using the tableau algorithm, which has to handle non-determinism. Prolog, with its efficient handling of non-determinism, is suitable for implementing the tableau algorithm. TRILL and TRILLP are systems offering a Prolog implementation of the tableau algorithm. TRILLP builds a pinpointing formula, that compactly represents the set of explanations and can be directly translated into a BDD. Both reasoners were shown to outperform state-of-the-art DL reasoners. In this paper, we present an improvement of TRILLP, named TORNADO, in which the BDD is directly built during the construction of the tableau, further speeding up the overall inference process. An experimental comparison shows the effectiveness of TORNADO. All systems can be tried online in the TRILL on SWISH web application at http://trill.ml.unife.it/.

cs.AI↗

SWISH: SWI-Prolog for Sharing

Recently, we see a new type of interfaces for programmers based on web technology. For example, JSFiddle, IPython Notebook and R-studio. Web technology enables cloud-based solutions, embedding in tutorial web pages, atractive rendering of results, web-scale cooperative development, etc. This article describes SWISH, a web front-end for Prolog. A public website exposes SWI-Prolog using SWISH, which is used to run small Prolog programs for demonstration, experimentation and education. We connected SWISH to the ClioPatria semantic web toolkit, where it allows for collaborative development of programs and queries related to a dataset as well as performing maintenance tasks on the running server and we embedded SWISH in the Learn Prolog Now! online Prolog book.

cs.PL↗

Lifted Variable Elimination for Probabilistic Logic Programming

Lifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances. Even if various authors have underlined its importance for probabilistic logic programming (PLP), lifted inference has been applied up to now only to relational languages outside of logic programming. In this paper we adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the problem of computing the probability of queries to probabilistic logic programs under the distribution semantics. In particular, we extend the Prolog Factor Language (PFL) to include two new types of factors that are needed for representing ProbLog programs. These factors take into account the existing causal independence relationships among random variables and are managed by the extension to variable elimination proposed by Zhang and Poole for dealing with convergent variables and heterogeneous factors. Two new operators are added to GC-FOVE for treating heterogeneous factors. The resulting algorithm, called LP$^2$ for Lifted Probabilistic Logic Programming, has been implemented by modifying the PFL implementation of GC-FOVE and tested on three benchmarks for lifted inference. A comparison with PITA and ProbLog2 shows the potential of the approach.

cs.AI↗

Structure Learning of Probabilistic Logic Programs by Searching the Clause Space

Learning probabilistic logic programming languages is receiving an increasing attention and systems are available for learning the parameters (PRISM, LeProbLog, LFI-ProbLog and EMBLEM) or both the structure and the parameters (SEM-CP-logic and SLIPCASE) of these languages. In this paper we present the algorithm SLIPCOVER for "Structure LearnIng of Probabilistic logic programs by searChing OVER the clause space". It performs a beam search in the space of probabilistic clauses and a greedy search in the space of theories, using the log likelihood of the data as the guiding heuristics. To estimate the log likelihood SLIPCOVER performs Expectation Maximization with EMBLEM. The algorithm has been tested on five real world datasets and compared with SLIPCASE, SEM-CP-logic, Aleph and two algorithms for learning Markov Logic Networks (Learning using Structural Motifs (LSM) and ALEPH++ExactL1). SLIPCOVER achieves higher areas under the precision-recall and ROC curves in most cases.

cs.LG↗

Well-Definedness and Efficient Inference for Probabilistic Logic Programming under the Distribution Semantics

The distribution semantics is one of the most prominent approaches for the combination of logic programming and probability theory. Many languages follow this semantics, such as Independent Choice Logic, PRISM, pD, Logic Programs with Annotated Disjunctions (LPADs) and ProbLog. When a program contains functions symbols, the distribution semantics is well-defined only if the set of explanations for a query is finite and so is each explanation. Well-definedness is usually either explicitly imposed or is achieved by severely limiting the class of allowed programs. In this paper we identify a larger class of programs for which the semantics is well-defined together with an efficient procedure for computing the probability of queries. Since LPADs offer the most general syntax, we present our results for them, but our results are applicable to all languages under the distribution semantics. We present the algorithm "Probabilistic Inference with Tabling and Answer subsumption" (PITA) that computes the probability of queries by transforming a probabilistic program into a normal program and then applying SLG resolution with answer subsumption. PITA has been implemented in XSB and tested on six domains: two with function symbols and four without. The execution times are compared with those of ProbLog, cplint and CVE, PITA was almost always able to solve larger problems in a shorter time, on domains with and without function symbols.

cs.AI↗

The PITA System: Tabling and Answer Subsumption for Reasoning under Uncertainty

Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic Programming (PLP), leading to languages such as the Independent Choice Logic, Logic Programs with Annotated Disjunctions (LPADs), Problog, PRISM and others. These languages share a similar distribution semantics, and methods have been devised to translate programs between these languages. The complexity of computing the probability of queries to these general PLP programs is very high due to the need to combine the probabilities of explanations that may not be exclusive. As one alternative, the PRISM system reduces the complexity of query answering by restricting the form of programs it can evaluate. As an entirely different alternative, Possibilistic Logic Programs adopt a simpler metric of uncertainty than probability. Each of these approaches -- general PLP, restricted PLP, and Possibilistic Logic Programming -- can be useful in different domains depending on the form of uncertainty to be represented, on the form of programs needed to model problems, and on the scale of the problems to be solved. In this paper, we show how the PITA system, which originally supported the general PLP language of LPADs, can also efficiently support restricted PLP and Possibilistic Logic Programs. PITA relies on tabling with answer subsumption and consists of a transformation along with an API for library functions that interface with answer subsumption.

cs.AI↗

Logic-Based Decision Support for Strategic Environmental Assessment

Strategic Environmental Assessment is a procedure aimed at introducing systematic assessment of the environmental effects of plans and programs. This procedure is based on the so-called coaxial matrices that define dependencies between plan activities (infrastructures, plants, resource extractions, buildings, etc.) and positive and negative environmental impacts, and dependencies between these impacts and environmental receptors. Up to now, this procedure is manually implemented by environmental experts for checking the environmental effects of a given plan or program, but it is never applied during the plan/program construction. A decision support system, based on a clear logic semantics, would be an invaluable tool not only in assessing a single, already defined plan, but also during the planning process in order to produce an optimized, environmentally assessed plan and to study possible alternative scenarios. We propose two logic-based approaches to the problem, one based on Constraint Logic Programming and one on Probabilistic Logic Programming that could be, in the future, conveniently merged to exploit the advantages of both. We test the proposed approaches on a real energy plan and we discuss their limitations and advantages.

cs.AI↗