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We propose an Expectation-Maximization (EM) algorithm which works on binary decision diagrams (BDDs). The proposed algorithm, BDD-EM algorithm, opens a way to apply BDDs to statistical learning. The BDD-EM algorithm makes it possible to learn probabilities in statistical models described by Boolean formulas, and the time complexity is proportional to the… (More)

Polynomial networks and factorization machines are two recently-proposed models that can efficiently use feature interactions in classification and regression tasks. In this paper, we revisit both models from a unified perspective. Based on this new view, we study the properties of both models and propose new efficient training algorithms. Key to our… (More)

Factorization machines (FMs) are a supervised learning approach that can use second-order feature combinations even when the data is very high-dimensional. Unfortunately, despite increasing interest in FMs, there exists to date no efficient training algorithm for higher-order FMs (HOFMs). In this paper, we present the first generic yet efficient algorithms… (More)

- Masakazu Ishihata, Taisuke Sato
- ACML
- 2011

Abduction is one of the basic logical inferences (deduction, induction and abduction) and derives the best explanations for our observation. Statistical abduction attempts to define a probability distribution over explanations and to evaluate them by their probabilities. The framework of statistical abduction is general since many well-known probabilistic… (More)

Evaluating influence spread in social networks is a fundamental procedure to estimate the word-of-mouth effect in viral marketing. There are enormous studies about this topic; however, under the standard stochastic cascade models, the exact computation of influence spread is known to be #P-hard. Thus, the existing studies have used Monte-Carlo… (More)

Abductive inference is an important AI reasoning technique to find explanations of observations, and has recently been applied to scientific discovery. To find best hypotheses among many logically possible hypotheses, we need to evaluate hypotheses obtained from the process of hypothesis generation. We propose an abductive inference architecture combined… (More)

- Gabriel Synnaeve, Katsumi Inoue, +4 authors Taisuke Sato
- BIOINFORMATICS
- 2011

This paper presents a method for enabling the relational learning or inductive logic programming (ILP) framework to deal with quantitative information from experimental data in systems biology. The study of systems biology through ILP aims at improving the understanding of the physiological state of the cell and the interpretation of the interactions… (More)

Logic-based probabilistic models (LBPMs) enable us to handle problems with uncertainty succinctly thanks to the expressive power of logic. However, most of LBPMs have restrictions to realize efficient probability computation and learning. We propose an EM algorithm working on BDDs with order encoding for LBPMs. A notable advantage of our algorithm over… (More)

Statistical abduction is an attempt to define a probability distribution over explanations derived by abduction and to evaluate them using their probabilities. In statistical abduction, deterministic knowledge like rules and facts are described as logic formulas. However nondeterministic knowledge like preference and frequency seems difficult to represent… (More)

- Masakazu Ishihata, Taisuke Sato, Shin-ichi Minato
- Australasian Conference on Artificial…
- 2011