Counting points on hyperelliptic curves with explicit real multiplication in arbitrary genus

We present a probabilistic Las Vegas algorithm for computing the local zeta function of a genus-$g$ hyperelliptic curve defined over $\mathbb F_q$ with explicit real multiplication (RM) by an order $\Z[\eta]$ in a degree-$g$ totally real number field. It is based on the approaches by Schoof and Pila in a more favorable case where we can split the $\ell$-torsion into $g$ kernels of endomorphisms, as introduced by Gaudry, Kohel, and Smith in genus 2. To deal with these kernels in any genus, we adapt a technique that the author, Gaudry, and Spaenlehauer introduced to model the $\ell$-torsion by structured polynomial systems. Applying this technique to the kernels, the systems we obtain are much smaller and so is the complexity of solving them. Our main result is that there exists a constant $c>0$ such that, for any fixed $g$, this algorithm has expected time and space complexity $O((\log q)^{c})$ as $q$ grows and the characteristic is large enough. We prove that $c\le 9$ and we also conjecture that the result still holds for $c=7$.Comment: To appear in Journal of Complexity. arXiv admin note: text overlap with arXiv:1710.0344

Probabilistic Graph Attention Network with Conditional Kernels for Pixel-Wise Prediction

Multi-scale representations deeply learned via convolutional neural networks have shown tremendous importance for various pixel-level prediction problems. In this paper we present a novel approach that advances the state of the art on pixel-level prediction in a fundamental aspect, i.e. structured multi-scale features learning and fusion. In contrast to previous works directly considering multi-scale feature maps obtained from the inner layers of a primary CNN architecture, and simply fusing the features with weighted averaging or concatenation, we propose a probabilistic graph attention network structure based on a novel Attention-Gated Conditional Random Fields (AG-CRFs) model for learning and fusing multi-scale representations in a principled manner. In order to further improve the learning capacity of the network structure, we propose to exploit feature dependant conditional kernels within the deep probabilistic framework. Extensive experiments are conducted on four publicly available datasets (i.e. BSDS500, NYUD-V2, KITTI, and Pascal-Context) and on three challenging pixel-wise prediction problems involving both discrete and continuous labels (i.e. monocular depth estimation, object contour prediction, and semantic segmentation). Quantitative and qualitative results demonstrate the effectiveness of the proposed latent AG-CRF model and the overall probabilistic graph attention network with feature conditional kernels for structured feature learning and pixel-wise prediction.Comment: Regular paper accepted at TPAMI 2020. arXiv admin note: text overlap with arXiv:1801.0052

Combining Thesaurus Knowledge and Probabilistic Topic Models

In this paper we present the approach of introducing thesaurus knowledge into probabilistic topic models. The main idea of the approach is based on the assumption that the frequencies of semantically related words and phrases, which are met in the same texts, should be enhanced: this action leads to their larger contribution into topics found in these texts. We have conducted experiments with several thesauri and found that for improving topic models, it is useful to utilize domain-specific knowledge. If a general thesaurus, such as WordNet, is used, the thesaurus-based improvement of topic models can be achieved with excluding hyponymy relations in combined topic models.Comment: Accepted to AIST-2017 conference (http://aistconf.ru/). The final publication will be available at link.springer.co

Transductive Learning with String Kernels for Cross-Domain Text Classification

For many text classification tasks, there is a major problem posed by the lack of labeled data in a target domain. Although classifiers for a target domain can be trained on labeled text data from a related source domain, the accuracy of such classifiers is usually lower in the cross-domain setting. Recently, string kernels have obtained state-of-the-art results in various text classification tasks such as native language identification or automatic essay scoring. Moreover, classifiers based on string kernels have been found to be robust to the distribution gap between different domains. In this paper, we formally describe an algorithm composed of two simple yet effective transductive learning approaches to further improve the results of string kernels in cross-domain settings. By adapting string kernels to the test set without using the ground-truth test labels, we report significantly better accuracy rates in cross-domain English polarity classification.Comment: Accepted at ICONIP 2018. arXiv admin note: substantial text overlap with arXiv:1808.0840

kLog: A Language for Logical and Relational Learning with Kernels

We introduce kLog, a novel approach to statistical relational learning. Unlike standard approaches, kLog does not represent a probability distribution directly. It is rather a language to perform kernel-based learning on expressive logical and relational representations. kLog allows users to specify learning problems declaratively. It builds on simple but powerful concepts: learning from interpretations, entity/relationship data modeling, logic programming, and deductive databases. Access by the kernel to the rich representation is mediated by a technique we call graphicalization: the relational representation is first transformed into a graph --- in particular, a grounded entity/relationship diagram. Subsequently, a choice of graph kernel defines the feature space. kLog supports mixed numerical and symbolic data, as well as background knowledge in the form of Prolog or Datalog programs as in inductive logic programming systems. The kLog framework can be applied to tackle the same range of tasks that has made statistical relational learning so popular, including classification, regression, multitask learning, and collective classification. We also report about empirical comparisons, showing that kLog can be either more accurate, or much faster at the same level of accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at http://klog.dinfo.unifi.it along with tutorials

Exploring Prediction Uncertainty in Machine Translation Quality Estimation

Machine Translation Quality Estimation is a notoriously difficult task, which lessens its usefulness in real-world translation environments. Such scenarios can be improved if quality predictions are accompanied by a measure of uncertainty. However, models in this task are traditionally evaluated only in terms of point estimate metrics, which do not take prediction uncertainty into account. We investigate probabilistic methods for Quality Estimation that can provide well-calibrated uncertainty estimates and evaluate them in terms of their full posterior predictive distributions. We also show how this posterior information can be useful in an asymmetric risk scenario, which aims to capture typical situations in translation workflows.Comment: Proceedings of CoNLL 201

Visual Dynamics: Probabilistic Future Frame Synthesis via Cross Convolutional Networks

We study the problem of synthesizing a number of likely future frames from a single input image. In contrast to traditional methods, which have tackled this problem in a deterministic or non-parametric way, we propose a novel approach that models future frames in a probabilistic manner. Our probabilistic model makes it possible for us to sample and synthesize many possible future frames from a single input image. Future frame synthesis is challenging, as it involves low- and high-level image and motion understanding. We propose a novel network structure, namely a Cross Convolutional Network to aid in synthesizing future frames; this network structure encodes image and motion information as feature maps and convolutional kernels, respectively. In experiments, our model performs well on synthetic data, such as 2D shapes and animated game sprites, as well as on real-wold videos. We also show that our model can be applied to tasks such as visual analogy-making, and present an analysis of the learned network representations.Comment: The first two authors contributed equally to this wor