Raffaele Giancarlo

Dario Malchiodi, Davide Raimondi, Giacomo Fumagalli et al.

Learned Bloom Filters, i.e., models induced from data via machine learning techniques and solving the approximate set membership problem, have recently been introduced with the aim of enhancing the performance of standard Bloom Filters, with special focus on space occupancy. Unlike in the classical case, the "complexity" of the data used to build the filter might heavily impact on its performance. Therefore, here we propose the first in-depth analysis, to the best of our knowledge, for the performance assessment of a given Learned Bloom Filter, in conjunction with a given classifier, on a dataset of a given classification complexity. Indeed, we propose a novel methodology, supported by software, for designing, analyzing and implementing Learned Bloom Filters in function of specific constraints on their multi-criteria nature (that is, constraints involving space efficiency, false positive rate, and reject time). Our experiments show that the proposed methodology and the supporting software are valid and useful: we find out that only two classifiers have desirable properties in relation to problems with different data complexity, and, interestingly, none of them has been considered so far in the literature. We also experimentally show that the Sandwiched variant of Learned Bloom filters is the most robust to data complexity and classifier performance variability, as well as those usually having smaller reject times. The software can be readily used to test new Learned Bloom Filter proposals, which can be compared with the best ones identified here.

Domenico Amato, Giosué Lo Bosco, Raffaele Giancarlo

This research concerns Learned Data Structures, a recent area that has emerged at the crossroad of Machine Learning and Classic Data Structures. It is methodologically important and with a high practical impact. We focus on Learned Indexes, i.e., Learned Sorted Set Dictionaries. The proposals available so far are specific in the sense that they can boost, indeed impressively, the time performance of Table Search Procedures with a sorted layout only, e.g., Binary Search. We propose a novel paradigm that, complementing known specialized ones, can produce Learned versions of any Sorted Set Dictionary, for instance, Balanced Binary Search Trees or Binary Search on layouts other that sorted, i.e., Eytzinger. Theoretically, based on it, we obtain several results of interest, such as (a) the first Learned Optimum Binary Search Forest, with mean access time bounded by the Entropy of the probability distribution of the accesses to the Dictionary; (b) the first Learned Sorted Set Dictionary that, in the Dynamic Case and in an amortized analysis setting, matches the same time bounds known for Classic Dictionaries. This latter under widely accepted assumptions regarding the size of the Universe. The experimental part, somewhat complex in terms of software development, clearly indicates the nonobvious finding that the generalization we propose can yield effective and competitive Learned Data Structural Booster, even with respect to specific benchmark models.

Domenico Amato, Giosue' Lo Bosco, Raffaele Giancarlo

With the aim of obtaining time/space improvements in classic Data Structures, an emerging trend is to combine Machine Learning techniques with the ones proper of Data Structures. This new area goes under the name of Learned Data Structures. The motivation for its study is a perceived change of paradigm in Computer Architectures that would favour the use of Graphics Processing Units and Tensor Processing Units over conventional Central Processing Units. In turn, that would favour the use of Neural Networks as building blocks of Classic Data Structures. Indeed, Learned Bloom Filters, which are one of the main pillars of Learned Data Structures, make extensive use of Neural Networks to improve the performance of classic Filters. However, no use of Neural Networks is reported in the realm of Learned Indexes, which is another main pillar of that new area. In this contribution, we provide the first, and much needed, comparative experimental analysis regarding the use of Neural Networks as building blocks of Learned Indexes. The results reported here highlight the need for the design of very specialized Neural Networks tailored to Learned Indexes and it establishes a solid ground for those developments. Our findings, methodologically important, are of interest to both Scientists and Engineers working in Neural Networks Design and Implementation, in view also of the importance of the application areas involved, e.g., Computer Networks and Data Bases.

Domenico Amato, Giosuè Lo Bosco, Raffaele Giancarlo

Learned Indexes are a novel approach to search in a sorted table. A model is used to predict an interval in which to search into and a Binary Search routine is used to finalize the search. They are quite effective. For the final stage, usually, the lower_bound routine of the Standard C++ library is used, although this is more of a natural choice rather than a requirement. However, recent studies, that do not use Machine Learning predictions, indicate that other implementations of Binary Search or variants, namely k-ary Search, are better suited to take advantage of the features offered by modern computer architectures. With the use of the Searching on Sorted Sets SOSD Learned Indexing benchmarking software, we investigate how to choose a Search routine for the final stage of searching in a Learned Index. Our results provide indications that better choices than the lower_bound routine can be made. We also highlight how such a choice may be dependent on the computer architecture that is to be used. Overall, our findings provide new and much-needed guidelines for the selection of the Search routine within the Learned Indexing framework.

Giacomo Fumagalli, Davide Raimondi, Raffaele Giancarlo et al.

Bloom Filters are a fundamental and pervasive data structure. Within the growing area of Learned Data Structures, several Learned versions of Bloom Filters have been considered, yielding advantages over classic Filters. Each of them uses a classifier, which is the Learned part of the data structure. Although it has a central role in those new filters, and its space footprint as well as classification time may affect the performance of the Learned Filter, no systematic study of which specific classifier to use in which circumstances is available. We report progress in this area here, providing also initial guidelines on which classifier to choose among five classic classification paradigms.

Domenico Amato, Giosuè Lo Bosco, Raffaele Giancarlo

Machine Learning Techniques, properly combined with Data Structures, have resulted in Learned Static Indexes, innovative and powerful tools that speed-up Binary Search, with the use of additional space with respect to the table being searched into. Such space is devoted to the Machine Learning Model. Although in their infancy, they are methodologically and practically important, due to the pervasiveness of Sorted Table Search procedures. In modern applications, model space is a key factor and, in fact, a major open question concerning this area is to assess to what extent one can enjoy the speed-up of Binary Search achieved by Learned Indexes while using constant or nearly constant space models. In this paper, we investigate the mentioned question by (a) introducing two new models, i.e., the Learned k-ary Search Model and the Synoptic Recursive Model Index, respectively; (b) systematically exploring the time-space trade-offs of a hierarchy of existing models, i.e., the ones in the reference software platform Searching on Sorted Data, together with the new ones proposed here. By adhering and extending the current benchmarking methodology, we experimentally show that the Learned k-ary Search Model can speed up Binary Search in constant additional space. Our second model, together with the bi-criteria Piece-wise Geometric Model index, can achieve a speed-up of Binary Search with a model space of 0:05% more than the one taken by the table, being competitive in terms of time-space trade-off with existing proposals. The Synoptic Recursive Model Index and the bi-criteria Piece-wise Geometric Model complement each other quite well across the various levels of the internal memory hierarchy. Finally, our findings stimulate research in this area, since they highlight the need for further studies regarding the time-space relation in Learned Indexes.

Domenico Amato, Giosué Lo Bosco, Raffaele Giancarlo

Sorted Table Search Procedures are the quintessential query-answering tool, with widespread usage that now includes also Web Applications, e.g, Search Engines (Google Chrome) and ad Bidding Systems (AppNexus). Speeding them up, at very little cost in space, is still a quite significant achievement. Here we study to what extend Machine Learning Techniques can contribute to obtain such a speed-up via a systematic experimental comparison of known efficient implementations of Sorted Table Search procedures, with different Data Layouts, and their Learned counterparts developed here. We characterize the scenarios in which those latter can be profitably used with respect to the former, accounting for both CPU and GPU computing. Our approach contributes also to the study of Learned Data Structures, a recent proposal to improve the time/space performance of fundamental Data Structures, e.g., B-trees, Hash Tables, Bloom Filters. Indeed, we also formalize an Algorithmic Paradigm of Learned Dichotomic Sorted Table Search procedures that naturally complements the Learned one proposed here and that characterizes most of the known Sorted Table Search Procedures as having a "learning phase" that approximates Simple Linear Regression.