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We analyze an extended model of the Iterated Prisoner's Dilemma where agents decide to play based on the data from their limited memory or on recommendation. The cooperators can decide whether to play with the matched opponent or not. The decisions of agents are directly linked to their optimism level since they decide to play if they believe the opponent has a high probability to cooperate. Optimism is precisely tuned by parameters named as optimism threshold and tolerance. Our experiment showed that being optimistic is better as it leads to more accurate judgments whereas acting pessimistic results in biased decisions.

A rapidly convergent series, based on Taylor expansion of the imaginary part of the complex error function, is presented for highly accurate approximation of the Voigt/complex error function with small imaginary argument (Y less than 0.1). Error analysis and run-time tests in double-precision computing platform reveals that in the real and imaginary parts the proposed algorithm provides average accuracy exceeding 10^-15 and 10^-16, respectively, and the calculation speed is as fast as that of reported in recent publications. An optimized MATLAB code providing rapid computation with high accuracy is presented.

We employ a toolset -- dubbed Dr. Frankenstein -- to analyse the similarity of representations in deep neural networks. With this toolset, we aim to match the activations on given layers of two trained neural networks by joining them with a stitching layer. We demonstrate that the inner representations emerging in deep convolutional neural networks with the same architecture but different initializations can be matched with a surprisingly high degree of accuracy even with a single, affine stitching layer. We choose the stitching layer from several possible classes of linear transformations and investigate their performance and properties. The task of matching representations is closely related to notions of similarity. Using this toolset, we also provide a novel viewpoint on the current line of research regarding similarity indices of neural network representations: the perspective of the performance on a task.

Recent works leveraging Graph Neural Networks to approach graph matching tasks have shown promising results. Recent progress in learning discrete distributions poses new opportunities for learning graph matching models. In this work, we propose a new model, Stochastic Iterative Graph MAtching (SIGMA), to address the graph matching problem. Our model defines a distribution of matchings for a graph pair so the model can explore a wide range of possible matchings. We further introduce a novel multi-step matching procedure, which learns how to refine a graph pair's matching results incrementally. The model also includes dummy nodes so that the model does not have to find matchings for nodes without correspondence. We fit this model to data via scalable stochastic optimization. We conduct extensive experiments across synthetic graph datasets as well as biochemistry and computer vision applications. Across all tasks, our results show that SIGMA can produce significantly improved graph matching results compared to state-of-the-art models. Ablation studies verify that each of our components (stochastic training, iterative matching, and dummy nodes) offers noticeable improvement.

The aim of this paper is to offer the first systematic exploration and definition of equivalent causal models in the context where both models are not made up of the same variables. The idea is that two models are equivalent when they agree on all "essential" causal information that can be expressed using their common variables. I do so by focussing on the two main features of causal models, namely their structural relations and their functional relations. In particular, I define several relations of causal ancestry and several relations of causal sufficiency, and require that the most general of these relations are preserved across equivalent models.

This paper seeks to develop a deeper understanding of the fundamental properties of neural text generations models. The study of artifacts that emerge in machine generated text as a result of modeling choices is a nascent research area. Previously, the extent and degree to which these artifacts surface in generated text has not been well studied. In the spirit of better understanding generative text models and their artifacts, we propose the new task of distinguishing which of several variants of a given model generated a piece of text, and we conduct an extensive suite of diagnostic tests to observe whether modeling choices (e.g., sampling methods, top-$k$ probabilities, model architectures, etc.) leave detectable artifacts in the text they generate. Our key finding, which is backed by a rigorous set of experiments, is that such artifacts are present and that different modeling choices can be inferred by observing the generated text alone. This suggests that neural text generators may be more sensitive to various modeling choices than previously thought.

This work focuses on mitigating two limitations in the joint learning of local feature detectors and descriptors. First, the ability to estimate the local shape (scale, orientation, etc.) of feature points is often neglected during dense feature extraction, while the shape-awareness is crucial to acquire stronger geometric invariance. Second, the localization accuracy of detected keypoints is not sufficient to reliably recover camera geometry, which has become the bottleneck in tasks such as 3D reconstruction. In this paper, we present ASLFeat, with three light-weight yet effective modifications to mitigate above issues. First, we resort to deformable convolutional networks to densely estimate and apply local transformation. Second, we take advantage of the inherent feature hierarchy to restore spatial resolution and low-level details for accurate keypoint localization. Finally, we use a peakiness measurement to relate feature responses and derive more indicative detection scores. The effect of each modification is thoroughly studied, and the evaluation is extensively conducted across a variety of practical scenarios. State-of-the-art results are reported that demonstrate the superiority of our methods.

Multispectral imaging is an important technique for improving the readability of written or printed text where the letters have faded, either due to deliberate erasing or simply due to the ravages of time. Often the text can be read simply by looking at individual wavelengths, but in some cases the images need further enhancement to maximise the chances of reading the text. There are many possible enhancement techniques and this paper assesses and compares an extended set of dimensionality reduction methods for image processing. We assess 15 dimensionality reduction methods in two different manuscripts. This assessment was performed both subjectively by asking the opinions of scholars who were experts in the languages used in the manuscripts which of the techniques they preferred and also by using the Davies-Bouldin and Dunn indexes for assessing the quality of the resulted image clusters. We found that the Canonical Variates Analysis (CVA) method which was using a Matlab implementation and we have used previously to enhance multispectral images, it was indeed superior to all the other tested methods. However it is very likely that other approaches will be more suitable in specific circumstance so we would still recommend that a range of these techniques are tried. In particular, CVA is a supervised clustering technique so it requires considerably more user time and effort than a non-supervised technique such as the much more commonly used Principle Component Analysis Approach (PCA). If the results from PCA are adequate to allow a text to be read then the added effort required for CVA may not be justified. For the purposes of comparing the computational times and the image results, a CVA method is also implemented in C programming language and using the GNU (GNUs Not Unix) Scientific Library (GSL) and the OpenCV (OPEN source Computer Vision) computer vision programming library.

Dynamic topic models (DTMs) model the evolution of prevalent themes in literature, online media, and other forms of text over time. DTMs assume that word co-occurrence statistics change continuously and therefore impose continuous stochastic process priors on their model parameters. These dynamical priors make inference much harder than in regular topic models, and also limit scalability. In this paper, we present several new results around DTMs. First, we extend the class of tractable priors from Wiener processes to the generic class of Gaussian processes (GPs). This allows us to explore topics that develop smoothly over time, that have a long-term memory or are temporally concentrated (for event detection). Second, we show how to perform scalable approximate inference in these models based on ideas around stochastic variational inference and sparse Gaussian processes. This way we can train a rich family of DTMs to massive data. Our experiments on several large-scale datasets show that our generalized model allows us to find interesting patterns that were not accessible by previous approaches.

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-specified rank. The algorithms are simple, accurate, numerically stable, and provably correct. Moreover, each method is accompanied by an informative error bound that allows users to select parameters a priori to achieve a given approximation quality. These claims are supported by numerical experiments with real and synthetic data.