A Bayesian Framework for Information-Theoretic Probing

Pimentel et al. (2020) recently analysed probing from an information-theoretic perspective. They argue that probing should be seen as approximating a mutual information. This led to the rather unintuitive conclusion that representations encode exactly the same information about a target task as the original sentences. The mutual information, however, assumes the true probability distribution of a pair of random variables is known, leading to unintuitive results in settings where it is not. This paper proposes a new framework to measure what we term Bayesian mutual information, which analyses information from the perspective of Bayesian agents---allowing for more intuitive findings in scenarios with finite data. For instance, under Bayesian MI we have that data can add information, processing can help, and information can hurt, which makes it more intuitive for machine learning applications. Finally, we apply our framework to probing where we believe Bayesian mutual information naturally operationalises ease of extraction by explicitly limiting the available background knowledge to solve a task.

Bayesian Model-Agnostic Meta-Learning with Matrix-Valued Kernels for Quality Estimation

Most current quality estimation (QE) models for machine translation are trained and evaluated in a fully supervised setting requiring significant quantities of labelled training data. However, obtaining labelled data can be both expensive and time-consuming. In addition, the test data that a deployed QE model would be exposed to may differ from its training data in significant ways. In particular, training samples are often labelled by one or a small set of annotators, whose perceptions of translation quality and needs may differ substantially from those of end-users, who will employ predictions in practice. Thus, it is desirable to be able to adapt QE models efficiently to new user data with limited supervision data. To address these challenges, we propose a Bayesian meta-learning approach for adapting QE models to the needs and preferences of each user with limited supervision. To enhance performance, we further propose an extension to a state-of-the-art Bayesian meta-learning approach which utilizes a matrix-valued kernel for Bayesian meta-learning of quality estimation. Experiments on data with varying number of users and language characteristics demonstrates that the proposed Bayesian meta-learning approach delivers improved predictive performance in both limited and full supervision settings.

From compositional semantics to Bayesian pragmatics via logical inference

Formal semantics in the Montagovian tradition provides precise meaning characterisations, but usually without a formal theory of the pragmatics of contextual parameters and their sensitivity to background knowledge. Meanwhile, formal pragmatic theories make explicit predictions about meaning in context, but generally without a well-defined compositional semantics. We propose a combined framework for the semantic and pragmatic interpretation of sentences in the face of probabilistic knowledge. We do so by (1) extending a Montagovian interpretation scheme to generate a distribution over possible meanings, and (2) generating a posterior for this distribution using a variant of the Rational Speech Act (RSA) models, but generalised to arbitrary propositions. These aspects of our framework are tied together by evaluating entailment under probabilistic uncertainty. We apply our model to anaphora resolution and show that it provides expected biases under suitable assumptions about the distributions of lexical and world-knowledge. Further, we observe that the model's output is robust to variations in its parameters within reasonable ranges.

Decision Making under Risk and Looking for the Optimal Strategies Based on the Available Information

In this paper, we will study the case of decision theory under risk and searching the optimal strategies which guarantee the maximum profits and minimum lost for the decision maker, In particular, we will study the random events which are under specific probability distribution. Based on the available information we will find the posterior distribution for the events using the Bayes’ rule. So we will try to find a mathematical method to minimize the risk rate.

Document Classification using Bayesian networks

أصبحت قضية استرجاع المعلومات في يومنا هذا من أهم القضايا والتحدّيات التي تشغل العالم كنتيجة منطقية للتطوّر التكنولوجي المتسارع والتقدم الهائل في الفكر الإنساني والبحوث والدراسات العلمية في شتى فروع المعرفة وما رافقه من ازدياد في كميات المعلومات إلى حدّ يصعب التحكم بها والتعامل معها. لذا نهدف في مشروعنا إلى تقديم نظام استرجاع معلومات يقوم بتصنيف المستندات حسب محتواها إلا أن عمليّة استرجاع المعلومات تحوي درجة من عدم التأكد في كل مرحلة من مراحلها لذا اعتمدنا على شبكات بيز للقيام بعملية التصنيف وهي شبكات احتماليّة تحوّل المعلومات إلى علاقات cause-and-effect و تعتبر واحدة من أهم الطرق الواعدة لمعالجة حالة عدم التأكد . في البدء نقوم بالتعريف بأساسيّات شبكات بيز ونشرح مجموعة من خوارزميّات بنائها وخوارزميّات الاستدلال المستخدمة ( ولها نوعان دقيق وتقريبي). يقوم هذه النظام بإجراء مجموعة من عمليّات المعالجة الأوليّة لنصوص المستندات ثم تطبيق عمليات إحصائية واحتمالية في مرحلة تدريب النظام والحصول على بنية شبكة بيز الموافقة لبيانات التدريب و يتم تصنيف مستند مدخل باستخدام مجموعة من خوارزميات الاستدلال الدقيق في شبكة بيز الناتجة لدينا. بما أنّ أداء أي نظام استرجاع معلومات عادة ما يزداد دقّة عند استخدام العلاقات بين المفردات (terms) المتضمّنة في مجموعة مستندات فسنأخذ بعين الاعتبار نوعين من العلاقات في بناء الشبكة: 1- العلاقات بين المفردات(terms). 2- العلاقات بين المفردات والأصناف(classes).