The problem of combining the evidence concerning an unknown, contained in each of $k$ Bayesian inference bases, is discussed. This can be considered as a generalization of the problem of pooling $k$ priors to determine a consensus prior. The linear opinion pool of Stone (1961) is seen to have the most appropriate properties for this role. In particular, linear pooling preserves a consensus with respect to the evidence and other rules do not. While linear pooling does not preserve prior independence, it is shown that it still behaves appropriately with respect to the expression of evidence in such a context. For the general problem of combining evidence, Jeffrey conditionalization plays a key role.
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Multilingual language models were shown to allow for nontrivial transfer across scripts and languages. In this work, we study the structure of the internal representations that enable this transfer. We focus on the representation of gender distinctions as a practical case study, and examine the extent to which the gender concept is encoded in shared subspaces across different languages. Our analysis shows that gender representations consist of several prominent components that are shared across languages, alongside language-specific components. The existence of language-independent and language-specific components provides an explanation for an intriguing empirical observation we make: while gender classification transfers well across languages, interventions for gender removal, trained on a single language, do not transfer easily to others.
Approximate-message passing (AMP) algorithms have become an important element of high-dimensional statistical inference, mostly due to their adaptability and concentration properties, the state evolution (SE) equations. This is demonstrated by the growing number of new iterations proposed for increasingly complex problems, ranging from multi-layer inference to low-rank matrix estimation with elaborate priors. In this paper, we address the following questions: is there a structure underlying all AMP iterations that unifies them in a common framework? Can we use such a structure to give a modular proof of state evolution equations, adaptable to new AMP iterations without reproducing each time the full argument ? We propose an answer to both questions, showing that AMP instances can be generically indexed by an oriented graph. This enables to give a unified interpretation of these iterations, independent from the problem they solve, and a way of composing them arbitrarily. We then show that all AMP iterations indexed by such a graph admit rigorous SE equations, extending the reach of previous proofs, and proving a number of recent heuristic derivations of those equations. Our proof naturally includes non-separable functions and we show how existing refinements, such as spatial coupling or matrix-valued variables, can be combined with our framework.
Faces play a central role in the combinatorial and computational aspects of polyhedra. In this paper, we present the first formalization of faces of polyhedra in the proof assistant Coq. This builds on the formalization of a library providing the basic constructions and operations over polyhedra, including projections, convex hulls and images under linear maps. Moreover, we design a special mechanism which automatically introduces an appropriate representation of a polyhedron or a face, depending on the context of the proof. We demonstrate the usability of this approach by establishing some of the most important combinatorial properties of faces, namely that they constitute a family of graded atomistic and coatomistic lattices closed under interval sublattices. We also prove a theorem due to Balinski on the $d$-connectedness of the adjacency graph of polytopes of dimension $d$.
Empirical results in software engineering have long started to show that findings are unlikely to be applicable to all software systems, or any domain: results need to be evaluated in specified contexts, and limited to the type of systems that they were extracted from. This is a known issue, and requires the establishment of a classification of software types. This paper makes two contributions: the first is to evaluate the quality of the current software classifications landscape. The second is to perform a case study showing how to create a classification of software types using a curated set of software systems. Our contributions show that existing, and very likely even new, classification attempts are deemed to fail for one or more issues, that we named as the `antipatterns' of software classification tasks. We collected 7 of these antipatterns that emerge from both our case study, and the existing classifications. These antipatterns represent recurring issues in a classification, so we discuss practical ways to help researchers avoid these pitfalls. It becomes clear that classification attempts must also face the daunting task of formulating a taxonomy of software types, with the objective of establishing a hierarchy of categories in a classification.
Self-Supervised Learning (SSL) models have been successfully applied in various deep learning-based speech tasks, particularly those with a limited amount of data. However, the quality of SSL representations depends highly on the relatedness between the SSL training domain(s) and the target data domain. On the contrary, spectral feature (SF) extractors such as log Mel-filterbanks are hand-crafted non-learnable components, and could be more robust to domain shifts. The present work examines the assumption that combining non-learnable SF extractors to SSL models is an effective approach to low resource speech tasks. We propose a learnable and interpretable framework to combine SF and SSL representations. The proposed framework outperforms significantly both baseline and SSL models on Automatic Speech Recognition (ASR) and Speech Translation (ST) tasks on three low resource datasets. We additionally design a mixture of experts based combination model. This last model reveals that the relative contribution of SSL models over conventional SF extractors is very small in case of domain mismatch between SSL training set and the target language data.
In this paper, we provide a general framework for studying multi-agent online learning problems in the presence of delays and asynchronicities. Specifically, we propose and analyze a class of adaptive dual averaging schemes in which agents only need to accumulate gradient feedback received from the whole system, without requiring any between-agent coordination. In the single-agent case, the adaptivity of the proposed method allows us to extend a range of existing results to problems with potentially unbounded delays between playing an action and receiving the corresponding feedback. In the multi-agent case, the situation is significantly more complicated because agents may not have access to a global clock to use as a reference point; to overcome this, we focus on the information that is available for producing each prediction rather than the actual delay associated with each feedback. This allows us to derive adaptive learning strategies with optimal regret bounds, even in a fully decentralized, asynchronous environment. Finally, we also analyze an "optimistic" variant of the proposed algorithm which is capable of exploiting the predictability of problems with a slower variation and leads to improved regret bounds.
We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting directions. Then we give a new information-theoretic proof of a finite version of de Finetti's classical representation theorem for finite-valued random variables. We derive an upper bound on the relative entropy between the distribution of the first $k$ in a sequence of $n$ exchangeable random variables, and an appropriate mixture over product distributions. The mixing measure is characterised as the law of the empirical measure of the original sequence, and de Finetti's result is recovered as a corollary. The proof is nicely motivated by the Gibbs conditioning principle in connection with statistical mechanics, and it follows along an appealing sequence of steps. The technical estimates required for these steps are obtained via the use of a collection of combinatorial tools known within information theory as `the method of types.'
Stickers with vivid and engaging expressions are becoming increasingly popular in online messaging apps, and some works are dedicated to automatically select sticker response by matching text labels of stickers with previous utterances. However, due to their large quantities, it is impractical to require text labels for the all stickers. Hence, in this paper, we propose to recommend an appropriate sticker to user based on multi-turn dialog context history without any external labels. Two main challenges are confronted in this task. One is to learn semantic meaning of stickers without corresponding text labels. Another challenge is to jointly model the candidate sticker with the multi-turn dialog context. To tackle these challenges, we propose a sticker response selector (SRS) model. Specifically, SRS first employs a convolutional based sticker image encoder and a self-attention based multi-turn dialog encoder to obtain the representation of stickers and utterances. Next, deep interaction network is proposed to conduct deep matching between the sticker with each utterance in the dialog history. SRS then learns the short-term and long-term dependency between all interaction results by a fusion network to output the the final matching score. To evaluate our proposed method, we collect a large-scale real-world dialog dataset with stickers from one of the most popular online chatting platform. Extensive experiments conducted on this dataset show that our model achieves the state-of-the-art performance for all commonly-used metrics. Experiments also verify the effectiveness of each component of SRS. To facilitate further research in sticker selection field, we release this dataset of 340K multi-turn dialog and sticker pairs.
Recent years have witnessed the enormous success of low-dimensional vector space representations of knowledge graphs to predict missing facts or find erroneous ones. Currently, however, it is not yet well-understood how ontological knowledge, e.g. given as a set of (existential) rules, can be embedded in a principled way. To address this shortcoming, in this paper we introduce a framework based on convex regions, which can faithfully incorporate ontological knowledge into the vector space embedding. Our technical contribution is two-fold. First, we show that some of the most popular existing embedding approaches are not capable of modelling even very simple types of rules. Second, we show that our framework can represent ontologies that are expressed using so-called quasi-chained existential rules in an exact way, such that any set of facts which is induced using that vector space embedding is logically consistent and deductively closed with respect to the input ontology.
Salient object detection is a problem that has been considered in detail and many solutions proposed. In this paper, we argue that work to date has addressed a problem that is relatively ill-posed. Specifically, there is not universal agreement about what constitutes a salient object when multiple observers are queried. This implies that some objects are more likely to be judged salient than others, and implies a relative rank exists on salient objects. The solution presented in this paper solves this more general problem that considers relative rank, and we propose data and metrics suitable to measuring success in a relative objects saliency landscape. A novel deep learning solution is proposed based on a hierarchical representation of relative saliency and stage-wise refinement. We also show that the problem of salient object subitizing can be addressed with the same network, and our approach exceeds performance of any prior work across all metrics considered (both traditional and newly proposed).
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