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A Short Introduction to Model Selection, Kolmogorov Complexity and Minimum Description Length (MDL)

The concept of overfitting in model selection is explained and demonstrated with an example. After providing some background information on information theory and Kolmogorov complexity, we provide a short explanation of Minimum Description Length and error minimization. We conclude with a discussion of the typical features of overfitting in model selection.

A multinomial probabilistic model for movie genre predictions

This paper proposes a movie genre-prediction based on multinomial probability model. To the best of our knowledge, this problem has not been addressed yet in the field of recommender system. The prediction of a movie genre has many practical applications including complementing the items categories given by experts and providing a surprise effect in the recommendations given to a user. We employ mulitnomial event model to estimate a likelihood of a movie given genre and the Bayes rule to evaluate the posterior probability of a genre given a movie. Experiments with the MovieLens dataset validate our approach. We achieved 70% prediction rate using only 15% of the whole set for training.

Addressing Community Question Answering in English and Arabic

This paper studies the impact of different types of features applied to learning to re-rank questions in community Question Answering. We tested our models on two datasets released in SemEval-2016 Task 3 on "Community Question Answering". Task 3 targeted real-life Web fora both in English and Arabic. Our models include bag-of-words features (BoW), syntactic tree kernels (TKs), rank features, embeddings, and machine translation evaluation features. To the best of our knowledge, structural kernels have barely been applied to the question reranking task, where they have to model paraphrase relations. In the case of the English question re-ranking task, we compare our learning to rank (L2R) algorithms against a strong baseline given by the Google-generated ranking (GR). The results show that i) the shallow structures used in our TKs are robust enough to noisy data and ii) improving GR is possible, but effective BoW features and TKs along with an accurate model of GR features in the used L2R algorithm are required. In the case of the Arabic question re-ranking task, for the first time we applied tree kernels on syntactic trees of Arabic sentences. Our approaches to both tasks obtained the second best results on SemEval-2016 subtasks B on English and D on Arabic.

Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition

We propose a simple two-step approach for speeding up convolution layers within large convolutional neural networks based on tensor decomposition and discriminative fine-tuning. Given a layer, we use non-linear least squares to compute a low-rank CP-decomposition of the 4D convolution kernel tensor into a sum of a small number of rank-one tensors. At the second step, this decomposition is used to replace the original convolutional layer with a sequence of four convolutional layers with small kernels. After such replacement, the entire network is fine-tuned on the training data using standard backpropagation process.

Park: An Open Platform for Learning-Augmented Computer Systems

We present Park, a platform for researchers to experiment with Reinforcement Learning (RL) for computer systems. Using RL for improving the performance of systems has a lot of potential, but is also in many ways very different from, for example, using RL for games. Thus, in this work we first discuss the unique challenges RL for systems has, and then propose Park an open extensible platform, which makes it easier for ML researchers to work on systems problems. Currently, Park consists of 12 real world system-centric optimization problems with one common easy to use interface. Finally, we present the performance of existing RL approaches over those 12 problems and outline potential areas of future work.

Freshman or Fresher? Quantifying the Geographic Variation of Internet Language

We present a new computational technique to detect and analyze statistically significant geographic variation in language. Our meta-analysis approach captures statistical properties of word usage across geographical regions and uses statistical methods to identify significant changes specific to regions. While previous approaches have primarily focused on lexical variation between regions, our method identifies words that demonstrate semantic and syntactic variation as well.

Using Artificial Neural Network Techniques for Prediction of Electric Energy Consumption

Due to imprecision and uncertainties in predicting real world problems, artificial neural network (ANN) techniques have become increasingly useful for modeling and optimization. This paper presents an artificial neural network approach for forecasting electric energy consumption. For effective planning and operation of power systems, optimal forecasting tools are needed for energy operators to maximize profit and also to provide maximum satisfaction to energy consumers. Monthly data for electric energy consumed in the Gaza strip was collected from year 1994 to 2013. Data was trained and the proposed model was validated using 2-Fold and K-Fold cross validation techniques. The model has been tested with actual energy consumption data and yields satisfactory performance.

Perturbative Black Box Variational Inference

Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with generalized divergences as a form of estimating the marginal likelihood via biased importance sampling. The choice of divergence determines a bias-variance trade-off between the tightness of a bound on the marginal likelihood (low bias) and the variance of its gradient estimators. Drawing on variational perturbation theory of statistical physics, we use these insights to construct a family of new variational bounds. Enumerated by an odd integer order $K$, this family captures the standard KL bound for $K=1$, and converges to the exact marginal likelihood as $K\to\infty$. Compared to alpha-divergences, our reparameterization gradients have a lower variance. We show in experiments on Gaussian Processes and Variational Autoencoders that the new bounds are more mass covering, and that the resulting posterior covariances are closer to the true posterior and lead to higher likelihoods on held-out data.

The Structurally Smoothed Graphlet Kernel

A commonly used paradigm for representing graphs is to use a vector that contains normalized frequencies of occurrence of certain motifs or sub-graphs. This vector representation can be used in a variety of applications, such as, for computing similarity between graphs. The graphlet kernel of Shervashidze et al. [32] uses induced sub-graphs of k nodes (christened as graphlets by Przulj [28]) as motifs in the vector representation, and computes the kernel via a dot product between these vectors. One can easily show that this is a valid kernel between graphs. However, such a vector representation suffers from a few drawbacks. As k becomes larger we encounter the sparsity problem; most higher order graphlets will not occur in a given graph. This leads to diagonal dominance, that is, a given graph is similar to itself but not to any other graph in the dataset. On the other hand, since lower order graphlets tend to be more numerous, using lower values of k does not provide enough discrimination ability. We propose a smoothing technique to tackle the above problems. Our method is based on a novel extension of Kneser-Ney and Pitman-Yor smoothing techniques from natural language processing to graphs. We use the relationships between lower order and higher order graphlets in order to derive our method. Consequently, our smoothing algorithm not only respects the dependency between sub-graphs but also tackles the diagonal dominance problem by distributing the probability mass across graphlets. In our experiments, the smoothed graphlet kernel outperforms graph kernels based on raw frequency counts.

Dynamic Filter Networks

In a traditional convolutional layer, the learned filters stay fixed after training. In contrast, we introduce a new framework, the Dynamic Filter Network, where filters are generated dynamically conditioned on an input. We show that this architecture is a powerful one, with increased flexibility thanks to its adaptive nature, yet without an excessive increase in the number of model parameters. A wide variety of filtering operation can be learned this way, including local spatial transformations, but also others like selective (de)blurring or adaptive feature extraction. Moreover, multiple such layers can be combined, e.g. in a recurrent architecture. We demonstrate the effectiveness of the dynamic filter network on the tasks of video and stereo prediction, and reach state-of-the-art performance on the moving MNIST dataset with a much smaller model. By visualizing the learned filters, we illustrate that the network has picked up flow information by only looking at unlabelled training data. This suggests that the network can be used to pretrain networks for various supervised tasks in an unsupervised way, like optical flow and depth estimation.

The Incredible Shrinking Neural Network: New Perspectives on Learning Representations Through The Lens of Pruning

How much can pruning algorithms teach us about the fundamentals of learning representations in neural networks? A lot, it turns out. Neural network model compression has become a topic of great interest in recent years, and many different techniques have been proposed to address this problem. In general, this is motivated by the idea that smaller models typically lead to better generalization. At the same time, the decision of what to prune and when to prune necessarily forces us to confront our assumptions about how neural networks actually learn to represent patterns in data. In this work we set out to test several long-held hypotheses about neural network learning representations and numerical approaches to pruning. To accomplish this we first reviewed the historical literature and derived a novel algorithm to prune whole neurons (as opposed to the traditional method of pruning weights) from optimally trained networks using a second-order Taylor method. We then set about testing the performance of our algorithm and analyzing the quality of the decisions it made. As a baseline for comparison we used a first-order Taylor method based on the Skeletonization algorithm and an exhaustive brute-force serial pruning algorithm. Our proposed algorithm worked well compared to a first-order method, but not nearly as well as the brute-force method. Our error analysis led us to question the validity of many widely-held assumptions behind pruning algorithms in general and the trade-offs we often make in the interest of reducing computational complexity. We discovered that there is a straightforward way, however expensive, to serially prune 40-70\% of the neurons in a trained network with minimal effect on the learning representation and without any re-training.

A Probabilistic Calculus of Actions

We present a symbolic machinery that admits both probabilistic and causal information about a given domain and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of conditioning operators: ordinary Bayes conditioning, P(y|X = x), which represents the observation X = x, and causal conditioning, P(y|do(X = x)), read the probability of Y = y conditioned on holding X constant (at x) by deliberate action. Given a mixture of such observational and causal sentences, together with the topology of the causal graph, the calculus derives new conditional probabilities of both types, thus enabling one to quantify the effects of actions (and policies) from partially specified knowledge bases, such as Bayesian networks in which some conditional probabilities may not be available.

FastBDT: A speed-optimized and cache-friendly implementation of stochastic gradient-boosted decision trees for multivariate classification

Stochastic gradient-boosted decision trees are widely employed for multivariate classification and regression tasks. This paper presents a speed-optimized and cache-friendly implementation for multivariate classification called FastBDT. FastBDT is one order of magnitude faster during the fitting-phase and application-phase, in comparison with popular implementations in software frameworks like TMVA, scikit-learn and XGBoost. The concepts used to optimize the execution time and performance studies are discussed in detail in this paper. The key ideas include: An equal-frequency binning on the input data, which allows replacing expensive floating-point with integer operations, while at the same time increasing the quality of the classification; a cache-friendly linear access pattern to the input data, in contrast to usual implementations, which exhibit a random access pattern. FastBDT provides interfaces to C/C++, Python and TMVA. It is extensively used in the field of high energy physics by the Belle II experiment.

Learning Mixtures of Ranking Models

This work concerns learning probabilistic models for ranking data in a heterogeneous population. The specific problem we study is learning the parameters of a Mallows Mixture Model. Despite being widely studied, current heuristics for this problem do not have theoretical guarantees and can get stuck in bad local optima. We present the first polynomial time algorithm which provably learns the parameters of a mixture of two Mallows models. A key component of our algorithm is a novel use of tensor decomposition techniques to learn the top-k prefix in both the rankings. Before this work, even the question of identifiability in the case of a mixture of two Mallows models was unresolved.

Towards a learning-theoretic analysis of spike-timing dependent plasticity

This paper suggests a learning-theoretic perspective on how synaptic plasticity benefits global brain functioning. We introduce a model, the selectron, that (i) arises as the fast time constant limit of leaky integrate-and-fire neurons equipped with spiking timing dependent plasticity (STDP) and (ii) is amenable to theoretical analysis. We show that the selectron encodes reward estimates into spikes and that an error bound on spikes is controlled by a spiking margin and the sum of synaptic weights. Moreover, the efficacy of spikes (their usefulness to other reward maximizing selectrons) also depends on total synaptic strength. Finally, based on our analysis, we propose a regularized version of STDP, and show the regularization improves the robustness of neuronal learning when faced with multiple stimuli.

Towards Understanding Sparse Filtering: A Theoretical Perspective

In this paper we present our study on a recent and effective algorithm for unsupervised learning, that is, sparse filtering. The aim of this research is not to show whether or how well sparse filtering works, but to understand why and when sparse filtering does work. We provide a thorough study of this algorithm through a conceptual evaluation of feature distribution learning, a theoretical analysis of the properties of sparse filtering, and an experimental validation of our conclusions. We argue that sparse filtering works by explicitly maximizing the informativeness of the learned representation through the maximization of the proxy of sparsity, and by implicitly preserving information conveyed by the distribution of the original data through the constraint of structure preservation. In particular, we prove that sparse filtering preserves the cosine neighborhoodness of the data. We validate our statements on artificial and real data sets by applying our theoretical understanding to the explanation of the success of sparse filtering on real-world problems. Our work provides a strong theoretical framework for understanding sparse filtering, it highlights assumptions and conditions for success behind the algorithm, and it provides a fresh insight into developing new feature distribution learning algorithms.

Experimental Support for a Categorical Compositional Distributional Model of Meaning

Modelling compositional meaning for sentences using empirical distributional methods has been a challenge for computational linguists. We implement the abstract categorical model of Coecke et al. (

Making Neural Programming Architectures Generalize via Recursion

Empirically, neural networks that attempt to learn programs from data have exhibited poor generalizability. Moreover, it has traditionally been difficult to reason about the behavior of these models beyond a certain level of input complexity. In order to address these issues, we propose augmenting neural architectures with a key abstraction: recursion. As an application, we implement recursion in the Neural Programmer-Interpreter framework on four tasks: grade-school addition, bubble sort, topological sort, and quicksort. We demonstrate superior generalizability and interpretability with small amounts of training data. Recursion divides the problem into smaller pieces and drastically reduces the domain of each neural network component, making it tractable to prove guarantees about the overall system’s behavior. Our experience suggests that in order for neural architectures to robustly learn program semantics, it is necessary to incorporate a concept like recursion.

Distributed Machine Learning via Sufficient Factor Broadcasting

Multiclass logistic regression (MLR) is a fundamental machine learning model to do multiclass classification. However, it is very challenging to perform MLR on large scale data where the feature dimension is high, the number of classes is large and the number of data samples is numerous. In this paper, we build a distributed framework to support large scale multiclass logistic regression. Using stochastic gradient descent to optimize MLR, we find that the gradient matrix is computed as the outer product of two vectors. This grants us an opportunity to greatly reduce communication cost: instead of communicating the gradient matrix among machines, we can only communicate the two vectors and use them to reconstruct the gradient matrix after communication. We design a Sufficient Vector Broadcaster (SVB) to support this communication pattern. SVB synchronizes the parameter matrix of MLR by broadcasting the sufficient vectors among machines and migrates gradient matrix computation on the receiver side.SVB can reduce the communication cost from quadratic to linear without incurring any loss of correctness. We evaluate the system on the ImageNet dataset and demonstrate the efficiency and effectiveness of our distributed framework.

Accelerating Exact and Approximate Inference for (Distributed) Discrete Optimization with GPUs

Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic variants such as Bayesian networks. Inference-based algorithms are powerful techniques for solving discrete optimization problems, which can be used independently or in combination with other techniques. However, their applicability is often limited by their compute intensive nature and their space requirements. This paper proposes the design and implementation of a novel inference-based technique, which exploits modern massively parallel architectures, such as those found in Graphical Processing Units (GPUs), to speed up the resolution of exact and approximated inference-based algorithms for discrete optimization. The paper studies the proposed algorithm in both centralized and distributed optimization contexts. The paper demonstrates that the use of GPUs provides significant advantages in terms of runtime and scalability, achieving up to two orders of magnitude in speedups and showing a considerable reduction in execution time (up to 345 times faster) with respect to a sequential version.

On Power-Law Kernels, Corresponding Reproducing Kernel Hilbert Space and Applications

The role of kernels is central to machine learning. Motivated by the importance of power law distributions in modeling, simulation and learning, in this paper, we propose a power-law generalization of the Gaussian kernel. This generalization is based on q-Gaussian distribution, which is a power-law distribution studied in context of nonextensive statistical mechanics. We prove that the proposed kernel is positive definite, and provide some insights regarding the corresponding Reproducing Kernel Hilbert Space (RKHS). We also study practical significance of q-Gaussian kernels in classification, regression and clustering, and present some simulation results.

Dimensionality Reduction for Stationary Time Series via Stochastic Nonconvex Optimization

Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies this fundamental challenge through a streaming PCA problem for stationary time series data. Specifically, our goal is to estimate the principle component of time series data with respect to the covariance matrix of the stationary distribution. Computationally, we propose a variant of Oja's algorithm combined with downsampling to control the bias of the stochastic gradient caused by the data dependency. Theoretically, we quantify the uncertainty of our proposed stochastic algorithm based on diffusion approximations. This allows us to prove the asymptotic rate of convergence and further implies near optimal asymptotic sample complexity. Numerical experiments are provided to support our analysis.

Preference Completion from Partial Rankings

We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of observed affinity values. Our approach exploits the observation that while preferences are often recorded as numerical scores, the predictive quantity of interest is the underlying rankings. Thus, attempts to closely match the recorded scores may lead to overfitting and impair generalization performance. Instead, we propose an estimator that directly fits the underlying preference order, combined with nuclear norm constraints to encourage low--rank parameters. Besides (approximate) correctness of the ranking order, the proposed estimator makes no generative assumption on the numerical scores of the observations. One consequence is that the proposed estimator can fit any consistent partial ranking over a subset of the items represented as a directed acyclic graph (DAG), generalizing standard techniques that can only fit preference scores. Despite this generality, for supervision representing total or blockwise total orders, the computational complexity of our algorithm is within a $\log$ factor of the standard algorithms for nuclear norm regularization based estimates for matrix completion. We further show promising empirical results for a novel and challenging application of collaboratively ranking of the associations between brain--regions and cognitive neuroscience terms.

Convergence Analysis of Prediction Markets via Randomized Subspace Descent

Prediction markets are economic mechanisms for aggregating information about future events through sequential interactions with traders. The pricing mechanisms in these markets are known to be related to optimization algorithms in machine learning and through these connections we have some understanding of how equilibrium market prices relate to the beliefs of the traders in a market. However, little is known about rates and guarantees for the convergence of these sequential mechanisms, and two recent papers cite this as an important open question.In this paper we show how some previously studied prediction market trading models can be understood as a natural generalization of randomized coordinate descent which we call randomized subspace descent (RSD). We establish convergence rates for RSD and leverage them to prove rates for the two prediction market models above, answering the open questions. Our results extend beyond standard centralized markets to arbitrary trade networks.

Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applications

Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known that the underlying structure of clean data is low-rank, but the exact rank of clean data is also known. Yet, when applying conventional rank minimization for those problems, the objective function is formulated in a way that does not fully utilize a priori target rank information about the problems. This observation motivates us to investigate whether there is a better alternative solution when using rank minimization. In this paper, instead of minimizing the nuclear norm, we propose to minimize the partial sum of singular values, which implicitly encourages the target rank constraint in rank minimization. Our experimental analyses show that, when the number of samples is deficient, our approach leads to a higher success rate than conventional rank minimization, while the solutions obtained by the two approaches are almost identical when the number of samples is more than sufficient. We apply our approach to various low-level vision problems, e.g. high dynamic range imaging, motion edge detection, photometric stereo, image alignment and recovery, and show that our results outperform those obtained by the conventional nuclear norm rank minimization method.

Prioritised Default Logic as Argumentation with Partial Order Default Priorities

We express Brewka's prioritised default logic (PDL) as argumentation using ASPIC+. By representing PDL as argumentation and designing an argument preference relation that takes the argument structure into account, we prove that the conclusions of the justified arguments correspond to the PDL extensions. We will first assume that the default priority is total, and then generalise to the case where it is a partial order. This provides a characterisation of non-monotonic inference in PDL as an exchange of argument and counter-argument, providing a basis for distributed non-monotonic reasoning in the form of dialogue.

A Natural Language Query Interface for Searching Personal Information on Smartwatches

Currently, personal assistant systems, run on smartphones and use natural language interfaces. However, these systems rely mostly on the web for finding information. Mobile and wearable devices can collect an enormous amount of contextual personal data such as sleep and physical activities. These information objects and their applications are known as quantified-self, mobile health or personal informatics, and they can be used to provide a deeper insight into our behavior. To our knowledge, existing personal assistant systems do not support all types of quantified-self queries. In response to this, we have undertaken a user study to analyze a set of "textual questions/queries" that users have used to search their quantified-self or mobile health data. Through analyzing these questions, we have constructed a light-weight natural language based query interface, including a text parser algorithm and a user interface, to process the users' queries that have been used for searching quantified-self information. This query interface has been designed to operate on small devices, i.e. smartwatches, as well as augmenting the personal assistant systems by allowing them to process end users' natural language queries about their quantified-self data.

Triple Generative Adversarial Nets

Generative Adversarial Nets (GANs) have shown promise in image generation and semi-supervised learning (SSL). However, existing GANs in SSL have two problems: (1) the generator and the discriminator (i.e. the classifier) may not be optimal at the same time; and (2) the generator cannot control the semantics of the generated samples. The problems essentially arise from the two-player formulation, where a single discriminator shares incompatible roles of identifying fake samples and predicting labels and it only estimates the data without considering the labels. To address the problems, we present triple generative adversarial net (Triple-GAN), which consists of three players---a generator, a discriminator and a classifier. The generator and the classifier characterize the conditional distributions between images and labels, and the discriminator solely focuses on identifying fake image-label pairs. We design compatible utilities to ensure that the distributions characterized by the classifier and the generator both converge to the data distribution. Our results on various datasets demonstrate that Triple-GAN as a unified model can simultaneously (1) achieve the state-of-the-art classification results among deep generative models, and (2) disentangle the classes and styles of the input and transfer smoothly in the data space via interpolation in the latent space class-conditionally.

The Power of Asymmetry in Binary Hashing

When approximating binary similarity using the hamming distance between short binary hashes, we show that even if the similarity is symmetric, we can have shorter and more accurate hashes by using two distinct code maps. I.e. by approximating the similarity between $x$ and $x'$ as the hamming distance between $f(x)$ and $g(x')$, for two distinct binary codes $f,g$, rather than as the hamming distance between $f(x)$ and $f(x')$.

Grounding Hierarchical Reinforcement Learning Models for Knowledge Transfer

Methods of deep machine learning enable to to reuse low-level representations efficiently for generating more abstract high-level representations. Originally, deep learning has been applied passively (e.g., for classification purposes). Recently, it has been extended to estimate the value of actions for autonomous agents within the framework of reinforcement learning (RL). Explicit models of the environment can be learned to augment such a value function. Although "flat" connectionist methods have already been used for model-based RL, up to now, only model-free variants of RL have been equipped with methods from deep learning. We propose a variant of deep model-based RL that enables an agent to learn arbitrarily abstract hierarchical representations of its environment. In this paper, we present research on how such hierarchical representations can be grounded in sensorimotor interaction between an agent and its environment.

Deep Mean-Shift Priors for Image Restoration

In this paper we introduce a natural image prior that directly represents a Gaussian-smoothed version of the natural image distribution. We include our prior in a formulation of image restoration as a Bayes estimator that also allows us to solve noise-blind image restoration problems. We show that the gradient of our prior corresponds to the mean-shift vector on the natural image distribution. In addition, we learn the mean-shift vector field using denoising autoencoders, and use it in a gradient descent approach to perform Bayes risk minimization. We demonstrate competitive results for noise-blind deblurring, super-resolution, and demosaicing.

Hierarchical Embeddings for Hypernymy Detection and Directionality

We present a novel neural model HyperVec to learn hierarchical embeddings for hypernymy detection and directionality. While previous embeddings have shown limitations on prototypical hypernyms, HyperVec represents an unsupervised measure where embeddings are learned in a specific order and capture the hypernym$-$hyponym distributional hierarchy. Moreover, our model is able to generalize over unseen hypernymy pairs, when using only small sets of training data, and by mapping to other languages. Results on benchmark datasets show that HyperVec outperforms both state$-$of$-$the$-$art unsupervised measures and embedding models on hypernymy detection and directionality, and on predicting graded lexical entailment.

Latent Attention Networks

Deep neural networks are able to solve tasks across a variety of domains and modalities of data. Despite many empirical successes, we lack the ability to clearly understand and interpret the learned internal mechanisms that contribute to such effective behaviors or, more critically, failure modes. In this work, we present a general method for visualizing an arbitrary neural network's inner mechanisms and their power and limitations. Our dataset-centric method produces visualizations of how a trained network attends to components of its inputs. The computed "attention masks" support improved interpretability by highlighting which input attributes are critical in determining output. We demonstrate the effectiveness of our framework on a variety of deep neural network architectures in domains from computer vision, natural language processing, and reinforcement learning. The primary contribution of our approach is an interpretable visualization of attention that provides unique insights into the network's underlying decision-making process irrespective of the data modality.

Learning Visual Servoing with Deep Features and Fitted Q-Iteration

Visual servoing involves choosing actions that move a robot in response to observations from a camera, in order to reach a goal configuration in the world. Standard visual servoing approaches typically rely on manually designed features and analytical dynamics models, which limits their generalization capability and often requires extensive application-specific feature and model engineering. In this work, we study how learned visual features, learned predictive dynamics models, and reinforcement learning can be combined to learn visual servoing mechanisms. We focus on target following, with the goal of designing algorithms that can learn a visual servo using low amounts of data of the target in question, to enable quick adaptation to new targets. Our approach is based on servoing the camera in the space of learned visual features, rather than image pixels or manually-designed keypoints. We demonstrate that standard deep features, in our case taken from a model trained for object classification, can be used together with a bilinear predictive model to learn an effective visual servo that is robust to visual variation, changes in viewing angle and appearance, and occlusions. A key component of our approach is to use a sample-efficient fitted Q-iteration algorithm to learn which features are best suited for the task at hand. We show that we can learn an effective visual servo on a complex synthetic car following benchmark using just 20 training trajectory samples for reinforcement learning. We demonstrate substantial improvement over a conventional approach based on image pixels or hand-designed keypoints, and we show an improvement in sample-efficiency of more than two orders of magnitude over standard model-free deep reinforcement learning algorithms. Videos are available at

Debiased Bayesian inference for average treatment effects

Bayesian approaches have become increasingly popular in causal inference problems due to their conceptual simplicity, excellent performance and in-built uncertainty quantification ('posterior credible sets'). We investigate Bayesian inference for average treatment effects from observational data, which is a challenging problem due to the missing counterfactuals and selection bias. Working in the standard potential outcomes framework, we propose a data-driven modification to an arbitrary (nonparametric) prior based on the propensity score that corrects for the first-order posterior bias, thereby improving performance. We illustrate our method for Gaussian process (GP) priors using (semi-)synthetic data. Our experiments demonstrate significant improvement in both estimation accuracy and uncertainty quantification compared to the unmodified GP, rendering our approach highly competitive with the state-of-the-art.

Simultaneous merging multiple grid maps using the robust motion averaging

Mapping in the GPS-denied environment is an important and challenging task in the field of robotics. In the large environment, mapping can be significantly accelerated by multiple robots exploring different parts of the environment. Accordingly, a key problem is how to integrate these local maps built by different robots into a single global map. In this paper, we propose an approach for simultaneous merging of multiple grid maps by the robust motion averaging. The main idea of this approach is to recover all global motions for map merging from a set of relative motions. Therefore, it firstly adopts the pair-wise map merging method to estimate relative motions for grid map pairs. To obtain as many reliable relative motions as possible, a graph-based sampling scheme is utilized to efficiently remove unreliable relative motions obtained from the pair-wise map merging. Subsequently, the accurate global motions can be recovered from the set of reliable relative motions by the motion averaging. Experimental results carried on real robot data sets demonstrate that proposed approach can achieve simultaneous merging of multiple grid maps with good performances.

Learning with a Wasserstein Loss

Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions. In this paper we develop a loss function for multi-label learning, based on the Wasserstein distance. The Wasserstein distance provides a natural notion of dissimilarity for probability measures. Although optimizing with respect to the exact Wasserstein distance is costly, recent work has described a regularized approximation that is efficiently computed. We describe efficient learning algorithms based on this regularization, extending the Wasserstein loss from probability measures to unnormalized measures. We also describe a statistical learning bound for the loss and show connections with the total variation norm and the Jaccard index. The Wasserstein loss can encourage smoothness of the predictions with respect to a chosen metric on the output space. We demonstrate this property on a real-data tag prediction problem, using the Yahoo Flickr Creative Commons dataset, achieving superior performance over a baseline that doesn't use the metric.

Optimal Sparsity-Sensitive Bounds for Distributed Mean Estimation

We consider the problem of estimating the mean of a set of vectors, which are stored in a distributed system. This is a fundamental task with applications in distributed SGD and many other distributed problems, where communication is a main bottleneck for scaling up computations. We propose a new sparsity-aware algorithm, which improves previous results both theoretically and empirically. The communication cost of our algorithm is characterized by Hoyer's measure of sparseness. Moreover, we prove that the communication cost of our algorithm is information-theoretic optimal up to a constant factor in all sparseness regime. We have also conducted experimental studies, which demonstrate the advantages of our method and confirm our theoretical findings.

FitNets: Hints for Thin Deep Nets

While depth tends to improve network performances, it also makes gradient-based training more difficult since deeper networks tend to be more non-linear. The recently proposed knowledge distillation approach is aimed at obtaining small and fast-to-execute models, and it has shown that a student network could imitate the soft output of a larger teacher network or ensemble of networks. In this paper, we extend this idea to allow the training of a student that is deeper and thinner than the teacher, using not only the outputs but also the intermediate representations learned by the teacher as hints to improve the training process and final performance of the student. Because the student intermediate hidden layer will generally be smaller than the teacher's intermediate hidden layer, additional parameters are introduced to map the student hidden layer to the prediction of the teacher hidden layer. This allows one to train deeper students that can generalize better or run faster, a trade-off that is controlled by the chosen student capacity. For example, on CIFAR-10, a deep student network with almost 10.4 times less parameters outperforms a larger, state-of-the-art teacher network.

Asymptotics for Sketching in Least Squares Regression

We consider a least squares regression problem where the data has been generated from a linear model, and we are interested to learn the unknown regression parameters. We consider "sketch-and-solve" methods that randomly project the data first, and do regression after. Previous works have analyzed the statistical and computational performance of such methods. However, the existing analysis is not fine-grained enough to show the fundamental differences between various methods, such as the Subsampled Randomized Hadamard Transform (SRHT) and Gaussian projections. In this paper, we make progress on this problem, working in an asymptotic framework where the number of datapoints and dimension of features goes to infinity. We find the limits of the accuracy loss (for estimation and test error) incurred by popular sketching methods. We show separation between different methods, so that SRHT is better than Gaussian projections. Our theoretical results are verified on both real and synthetic data. The analysis of SRHT relies on novel methods from random matrix theory that may be of independent interest.

Two-Manifold Problems

Recently, there has been much interest in spectral approaches to learning manifolds---so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To address this limitation, we look at two-manifold problems, in which we simultaneously reconstruct two related manifolds, each representing a different view of the same data. By solving these interconnected learning problems together and allowing information to flow between them, two-manifold algorithms are able to succeed where a non-integrated approach would fail: each view allows us to suppress noise in the other, reducing bias in the same way that an instrumental variable allows us to remove bias in a {linear} dimensionality reduction problem. We propose a class of algorithms for two-manifold problems, based on spectral decomposition of cross-covariance operators in Hilbert space. Finally, we discuss situations where two-manifold problems are useful, and demonstrate that solving a two-manifold problem can aid in learning a nonlinear dynamical system from limited data.

Sentence Ordering using Recurrent Neural Networks

Modeling the structure of coherent texts is a task of great importance in NLP. The task of organizing a given set of sentences into a coherent order has been commonly used to build and evaluate models that understand such structure. In this work we propose an end-to-end neural approach based on the recently proposed set to sequence mapping framework to address the sentence ordering problem. Our model achieves state-of-the-art performance in the order discrimination task on two datasets widely used in the literature. We also consider a new interesting task of ordering abstracts from conference papers and research proposals and demonstrate strong performance against recent methods. Visualizing the sentence representations learned by the model shows that the model has captured high level logical structure in these paragraphs. The model also learns rich semantic sentence representations by learning to order texts, performing comparably to recent unsupervised representation learning methods in the sentence similarity and paraphrase detection tasks.

Variational Autoencoders for Semi-supervised Text Classification

Semi-supervised learning becomes one of the most significant problems nowadays since the size of datasets is increasing tremendously while labeled data is limited. We propose a new semi-supervised learning method for sequence classification tasks. Our work is based on both deep generative model for semi-supervised learning \cite{kingma2014semi} and variational auto-encoder for sequence modeling \cite{bowman2015generating}. We found the introduction of Sc-LSTM is critical to the success in our method. We have obtained some preliminary experimental results on IMDB sentiment classification dataset, showing that the proposed model improves the classification accuracy comparing to pure supervised classifier.

Local minima in training of deep networks

There has been a lot of recent interest in trying to characterize the error surface of deep models. This stems from a long standing question. Given that deep networks are highly nonlinear systems optimized by local gradient methods, why do they not seem to be affected by bad local minima? It is widely believed that training of deep models using gradient methods works so well because the error surface either has no local minima, or if they exist they need to be close in value to the global minimum. It is known that such results hold under strong assumptions which are not satisfied by real models. In this paper we present examples showing that for such theorem to be true additional assumptions on the data, initialization schemes and/or the model classes have to be made. We look at the particular case of finite size datasets. We demonstrate that in this scenario one can construct counter-examples (datasets or initialization schemes) when the network does become susceptible to bad local minima over the weight space.

Classification-based Financial Markets Prediction using Deep Neural Networks

Deep neural networks (DNNs) are powerful types of artificial neural networks (ANNs) that use several hidden layers. They have recently gained considerable attention in the speech transcription and image recognition community (Krizhevsky et al., 2012) for their superior predictive properties including robustness to overfitting. However their application to algorithmic trading has not been previously researched, partly because of their computational complexity. This paper describes the application of DNNs to predicting financial market movement directions. In particular we describe the configuration and training approach and then demonstrate their application to backtesting a simple trading strategy over 43 different Commodity and FX future mid-prices at 5-minute intervals. All results in this paper are generated using a C++ implementation on the Intel Xeon Phi co-processor which is 11.4x faster than the serial version and a Python strategy backtesting environment both of which are available as open source code written by the authors.

Tractable Triangles and Cross-Free Convexity in Discrete Optimisation

The minimisation problem of a sum of unary and pairwise functions of discrete variables is a general NP-hard problem with wide applications such as computing MAP configurations in Markov Random Fields (MRF), minimising Gibbs energy, or solving binary Valued Constraint Satisfaction Problems (VCSPs).

Semi-Supervised Learning for Detecting Human Trafficking

Human trafficking is one of the most atrocious crimes and among the challenging problems facing law enforcement which demands attention of global magnitude. In this study, we leverage textual data from the website "Backpage"- used for classified advertisement- to discern potential patterns of human trafficking activities which manifest online and identify advertisements of high interest to law enforcement. Due to the lack of ground truth, we rely on a human analyst from law enforcement, for hand-labeling a small portion of the crawled data. We extend the existing Laplacian SVM and present S3VM-R, by adding a regularization term to exploit exogenous information embedded in our feature space in favor of the task at hand. We train the proposed method using labeled and unlabeled data and evaluate it on a fraction of the unlabeled data, herein referred to as unseen data, with our expert's further verification. Results from comparisons between our method and other semi-supervised and supervised approaches on the labeled data demonstrate that our learner is effective in identifying advertisements of high interest to law enforcement

Modeling Word Relatedness in Latent Dirichlet Allocation

Standard LDA model suffers the problem that the topic assignment of each word is independent and word correlation hence is neglected. To address this problem, in this paper, we propose a model called Word Related Latent Dirichlet Allocation (WR-LDA) by incorporating word correlation into LDA topic models. This leads to new capabilities that standard LDA model does not have such as estimating infrequently occurring words or multi-language topic modeling. Experimental results demonstrate the effectiveness of our model compared with standard LDA.

Learning Multiagent Communication with Backpropagation

Many tasks in AI require the collaboration of multiple agents. Typically, the communication protocol between agents is manually specified and not altered during training. In this paper we explore a simple neural model, called CommNN, that uses continuous communication for fully cooperative tasks. The model consists of multiple agents and the communication between them is learned alongside their policy. We apply this model to a diverse set of tasks, demonstrating the ability of the agents to learn to communicate amongst themselves, yielding improved performance over non-communicative agents and baselines. In some cases, it is possible to interpret the language devised by the agents, revealing simple but effective strategies for solving the task at hand.

Exploiting Multi-typed Treebanks for Parsing with Deep Multi-task Learning

Various treebanks have been released for dependency parsing. Despite that treebanks may belong to different languages or have different annotation schemes, they contain syntactic knowledge that is potential to benefit each other. This paper presents an universal framework for exploiting these multi-typed treebanks to improve parsing with deep multi-task learning. We consider two kinds of treebanks as source: the multilingual universal treebanks and the monolingual heterogeneous treebanks. Multiple treebanks are trained jointly and interacted with multi-level parameter sharing. Experiments on several benchmark datasets in various languages demonstrate that our approach can make effective use of arbitrary source treebanks to improve target parsing models.

Deep Reinforcement Learning for Multi-Domain Dialogue Systems

Standard deep reinforcement learning methods such as Deep Q-Networks (DQN) for multiple tasks (domains) face scalability problems. We propose a method for multi-domain dialogue policy learning---termed NDQN, and apply it to an information-seeking spoken dialogue system in the domains of restaurants and hotels. Experimental results comparing DQN (baseline) versus NDQN (proposed) using simulations report that our proposed method exhibits better scalability and is promising for optimising the behaviour of multi-domain dialogue systems.

Learning Graphical State Transitions

Graph-structured data is important in modeling relationships between multiple entities, and can be used to represent states of the world as well as many data structures. Li et al. (2016) describe a model known as a Gated Graph Sequence Neural Network (GGS-NN) that produces sequences from graph-structured input. In this work I introduce the Gated Graph Transformer Neural Network (GGT-NN), an extension of GGS-NNs that uses graph-structured data as an intermediate representation. The model can learn to construct and modify graphs in sophisticated ways based on textual input, and also to use the graphs to produce a variety of outputs. For example, the model successfully learns to solve almost all of the bAbI tasks (Weston et al., 2016), and also discovers the rules governing graphical formulations of a simple cellular automaton and a family of Turing machines.

N-Gram Graph: Simple Unsupervised Representation for Graphs, with Applications to Molecules

Machine learning techniques have recently been adopted in various applications in medicine, biology, chemistry, and material engineering. An important task is to predict the properties of molecules, which serves as the main subroutine in many downstream applications such as virtual screening and drug design. Despite the increasing interest, the key challenge is to construct proper representations of molecules for learning algorithms. This paper introduces the N-gram graph, a simple unsupervised representation for molecules. The method first embeds the vertices in the molecule graph. It then constructs a compact representation for the graph by assembling the vertex embeddings in short walks in the graph, which we show is equivalent to a simple graph neural network that needs no training. The representations can thus be efficiently computed and then used with supervised learning methods for prediction. Experiments on 60 tasks from 10 benchmark datasets demonstrate its advantages over both popular graph neural networks and traditional representation methods. This is complemented by theoretical analysis showing its strong representation and prediction power.

Finding a sparse vector in a subspace: Linear sparsity using alternating directions

We consider the problem of recovering the sparsest vector in a subspace $\mathcal{S} \subseteq \mathbb{R}^p$ with $\mathrm{dim}(\mathcal{S}) = n < p$. This problem can be considered a homogeneous variant of the sparse recovery problem, and finds applications in sparse dictionary learning, sparse PCA, and other problems in signal processing and machine learning. Simple convex heuristics for this problem provably break down when the fraction of nonzero entries in the target sparse vector substantially exceeds $1/\sqrt{n}$. In contrast, we exhibit a relatively simple nonconvex approach based on alternating directions, which provably succeeds even when the fraction of nonzero entries is $\Omega(1)$. To our knowledge, this is the first practical algorithm to achieve this linear scaling. This result assumes a planted sparse model, in which the target sparse vector is embedded in an otherwise random subspace. Empirically, our proposed algorithm also succeeds in more challenging data models arising, e.g., from sparse dictionary learning.

An Automatic Approach for Document-level Topic Model Evaluation

Topic models jointly learn topics and document-level topic distribution. Extrinsic evaluation of topic models tends to focus exclusively on topic-level evaluation, e.g. by assessing the coherence of topics. We demonstrate that there can be large discrepancies between topic- and document-level model quality, and that basing model evaluation on topic-level analysis can be highly misleading. We propose a method for automatically predicting topic model quality based on analysis of document-level topic allocations, and provide empirical evidence for its robustness.

Object category understanding via eye fixations on freehand sketches

The study of eye gaze fixations on photographic images is an active research area. In contrast, the image subcategory of freehand sketches has not received as much attention for such studies. In this paper, we analyze the results of a free-viewing gaze fixation study conducted on 3904 freehand sketches distributed across 160 object categories. Our analysis shows that fixation sequences exhibit marked consistency within a sketch, across sketches of a category and even across suitably grouped sets of categories. This multi-level consistency is remarkable given the variability in depiction and extreme image content sparsity that characterizes hand-drawn object sketches. In our paper, we show that the multi-level consistency in the fixation data can be exploited to (a) predict a test sketch's category given only its fixation sequence and (b) build a computational model which predicts part-labels underlying fixations on objects. We hope that our findings motivate the community to deem sketch-like representations worthy of gaze-based studies vis-a-vis photographic images.

Convergence of Gradient EM on Multi-component Mixture of Gaussians

In this paper, we study convergence properties of the gradient variant of Expectation-Maximization algorithm~\cite{lange1995gradient} for Gaussian Mixture Models for arbitrary number of clusters and mixing coefficients. We derive the convergence rate depending on the mixing coefficients, minimum and maximum pairwise distances between the true centers, dimensionality and number of components; and obtain a near-optimal local contraction radius. While there have been some recent notable works that derive local convergence rates for EM in the two symmetric mixture of Gaussians, in the more general case, the derivations need structurally different and non-trivial arguments. We use recent tools from learning theory and empirical processes to achieve our theoretical results.

Joint Sub-bands Learning with Clique Structures for Wavelet Domain Super-Resolution

Convolutional neural networks (CNNs) have recently achieved great success in single-image super-resolution (SISR). However, these methods tend to produce over-smoothed outputs and miss some textural details. To solve these problems, we propose the Super-Resolution CliqueNet (SRCliqueNet) to reconstruct the high resolution (HR) image with better textural details in the wavelet domain. The proposed SRCliqueNet firstly extracts a set of feature maps from the low resolution (LR) image by the clique blocks group. Then we send the set of feature maps to the clique up-sampling module to reconstruct the HR image. The clique up-sampling module consists of four sub-nets which predict the high resolution wavelet coefficients of four sub-bands. Since we consider the edge feature properties of four sub-bands, the four sub-nets are connected to the others so that they can learn the coefficients of four sub-bands jointly. Finally we apply inverse discrete wavelet transform (IDWT) to the output of four sub-nets at the end of the clique up-sampling module to increase the resolution and reconstruct the HR image. Extensive quantitative and qualitative experiments on benchmark datasets show that our method achieves superior performance over the state-of-the-art methods.

A convex program for bilinear inversion of sparse vectors

We consider the bilinear inverse problem of recovering two vectors, x in R^L and w in R^L, from their entrywise product. We consider the case where x and w have known signs and are sparse with respect to known dictionaries of size K and N, respectively. Here, K and N may be larger than, smaller than, or equal to L. We introduce L1-BranchHull, which is a convex program posed in the natural parameter space and does not require an approximate solution or initialization in order to be stated or solved. We study the case where x and w are S1- and S2-sparse with respect to a random dictionary, with the sparse vectors satisfying an effective sparsity condition, and present a recovery guarantee that depends on the number of measurements as L > Omega(S1+S2)(log(K+N))^2. Numerical experiments verify that the scaling constant in the theorem is not too large. One application of this problem is the sweep distortion removal task in dielectric imaging, where one of the signals is a nonnegative reflectivity, and the other signal lives in a known subspace, for example that given by dominant wavelet coefficients. We also introduce a variants of L1-BranchHull for the purposes of tolerating noise and outliers, and for the purpose of recovering piecewise constant signals. We provide an ADMM implementation of these variants and show they can extract piecewise constant behavior from real images.

VideoCapsuleNet: A Simplified Network for Action Detection

The recent advances in Deep Convolutional Neural Networks (DCNNs) have shown extremely good results for video human action classification, however, action detection is still a challenging problem. The current action detection approaches follow a complex pipeline which involves multiple tasks such as tube proposals, optical flow, and tube classification. In this work, we present a more elegant solution for action detection based on the recently developed capsule network. We propose a 3D capsule network for videos, called VideoCapsuleNet: a unified network for action detection which can jointly perform pixel-wise action segmentation along with action classification. The proposed network is a generalization of capsule network from 2D to 3D, which takes a sequence of video frames as input. The 3D generalization drastically increases the number of capsules in the network, making capsule routing computationally expensive. We introduce capsule-pooling in the convolutional capsule layer to address this issue and make the voting algorithm tractable. The routing-by-agreement in the network inherently models the action representations and various action characteristics are captured by the predicted capsules. This inspired us to utilize the capsules for action localization and the class-specific capsules predicted by the network are used to determine a pixel-wise localization of actions. The localization is further improved by parameterized skip connections with the convolutional capsule layers and the network is trained end-to-end with a classification as well as localization loss. The proposed network achieves state-of-the-art performance on multiple action detection datasets including UCF-Sports, J-HMDB, and UCF-101 (24 classes) with an impressive ~20% improvement on UCF-101 and ~15% improvement on J-HMDB in terms of v-mAP scores.

On Markov Chain Gradient Descent

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a variant of stochastic gradient descent where the random samples are taken on the trajectory of a Markov chain. Existing results of this method assume convex objectives and a reversible Markov chain and thus have their limitations. We establish new non-ergodic convergence under wider step sizes, for nonconvex problems, and for non-reversible finite-state Markov chains. Nonconvexity makes our method applicable to broader problem classes. Non-reversible finite-state Markov chains, on the other hand, can mix substatially faster. To obtain these results, we introduce a new technique that varies the mixing levels of the Markov chains. The reported numerical results validate our contributions.

Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach

In this paper we address the problem of decision making within a Markov decision process (MDP) framework where risk and modeling errors are taken into account. Our approach is to minimize a risk-sensitive conditional-value-at-risk (CVaR) objective, as opposed to a standard risk-neutral expectation. We refer to such problem as CVaR MDP. Our first contribution is to show that a CVaR objective, besides capturing risk sensitivity, has an alternative interpretation as expected cost under worst-case modeling errors, for a given error budget. This result, which is of independent interest, motivates CVaR MDPs as a unifying framework for risk-sensitive and robust decision making. Our second contribution is to present a value-iteration algorithm for CVaR MDPs, and analyze its convergence rate. To our knowledge, this is the first solution algorithm for CVaR MDPs that enjoys error guarantees. Finally, we present results from numerical experiments that corroborate our theoretical findings and show the practicality of our approach.

An Analysis of Tournament Structure

This paper explores a novel way for analyzing the tournament structures to find a best suitable one for the tournament under consideration. It concerns about three aspects such as tournament conducting cost, competitiveness development and ranking precision. It then proposes a new method using progress tree to detect potential throwaway matches. The analysis performed using the proposed method reveals the strengths and weaknesses of tournament structures. As a conclusion, single elimination is best if we want to qualify one winner only, all matches conducted are exciting in term of competitiveness. Double elimination with proper seeding system is a better choice if we want to qualify more winners. A reasonable number of extra matches need to be conducted in exchange of being able to qualify top four winners. Round-robin gives reliable ranking precision for all participants. However, its conduction cost is very high, and it fails to maintain competitiveness development.

Can neural machine translation do simultaneous translation?

We investigate the potential of attention-based neural machine translation in simultaneous translation. We introduce a novel decoding algorithm, called simultaneous greedy decoding, that allows an existing neural machine translation model to begin translating before a full source sentence is received. This approach is unique from previous works on simultaneous translation in that segmentation and translation are done jointly to maximize the translation quality and that translating each segment is strongly conditioned on all the previous segments. This paper presents a first step toward building a full simultaneous translation system based on neural machine translation.

Stochastic Variance Reduced Primal Dual Algorithms for Empirical Composition Optimization

We consider a generic empirical composition optimization problem, where there are empirical averages present both outside and inside nonlinear loss functions. Such a problem is of interest in various machine learning applications, and cannot be directly solved by standard methods such as stochastic gradient descent (SGD). We take a novel approach to solving this problem by reformulating the original minimization objective into an equivalent min-max objective, which brings out all the empirical averages that are originally inside the nonlinear loss functions. We exploit the rich structures of the reformulated problem and develop a stochastic primal-dual algorithms, SVRPDA-I, to solve the problem efficiently. We carry out extensive theoretical analysis of the proposed algorithm, obtaining the convergence rate, the total computation complexity and the storage complexity. In particular, the algorithm is shown to converge at a linear rate when the problem is strongly convex. Moreover, we also develop an approximate version of the algorithm, named SVRPDA-II, which further reduces the memory requirement. Finally, we evaluate the performance of our algorithms on several real-world benchmarks and experimental results show that they significantly outperform existing techniques.

Theano-MPI: a Theano-based Distributed Training Framework

We develop a scalable and extendable training framework that can utilize GPUs across nodes in a cluster and accelerate the training of deep learning models based on data parallelism. Both synchronous and asynchronous training are implemented in our framework, where parameter exchange among GPUs is based on CUDA-aware MPI. In this report, we analyze the convergence and capability of the framework to reduce training time when scaling the synchronous training of AlexNet and GoogLeNet from 2 GPUs to 8 GPUs. In addition, we explore novel ways to reduce the communication overhead caused by exchanging parameters. Finally, we release the framework as open-source for further research on distributed deep learning

Convolutional Neural Networks for joint object detection and pose estimation: A comparative study

In this paper we study the application of convolutional neural networks for jointly detecting objects depicted in still images and estimating their 3D pose. We identify different feature representations of oriented objects, and energies that lead a network to learn this representations. The choice of the representation is crucial since the pose of an object has a natural, continuous structure while its category is a discrete variable. We evaluate the different approaches on the joint object detection and pose estimation task of the Pascal3D+ benchmark using Average Viewpoint Precision. We show that a classification approach on discretized viewpoints achieves state-of-the-art performance for joint object detection and pose estimation, and significantly outperforms existing baselines on this benchmark.

Learning Topic-Sensitive Word Representations

Distributed word representations are widely used for modeling words in NLP tasks. Most of the existing models generate one representation per word and do not consider different meanings of a word. We present two approaches to learn multiple topic-sensitive representations per word by using Hierarchical Dirichlet Process. We observe that by modeling topics and integrating topic distributions for each document we obtain representations that are able to distinguish between different meanings of a given word. Our models yield statistically significant improvements for the lexical substitution task indicating that commonly used single word representations, even when combined with contextual information, are insufficient for this task.

A Joint Many-Task Model: Growing a Neural Network for Multiple NLP Tasks

Transfer and multi-task learning have traditionally focused on either a single source-target pair or very few, similar tasks. Ideally, the linguistic levels of morphology, syntax and semantics would benefit each other by being trained in a single model. We introduce such a joint many-task model together with a strategy for successively growing its depth to solve increasingly complex tasks. All layers include shortcut connections to both word representations and lower-level task predictions. We use a simple regularization term to allow for optimizing all model weights to improve one task's loss without exhibiting catastrophic interference of the other tasks. Our single end-to-end trainable model obtains state-of-the-art results on chunking, dependency parsing, semantic relatedness and textual entailment. It also performs competitively on POS tagging. Our dependency parsing layer relies only on a single feed-forward pass and does not require a beam search.

Scheduling a Dynamic Aircraft Repair Shop with Limited Repair Resources

We address a dynamic repair shop scheduling problem in the context of military aircraft fleet management where the goal is to maintain a full complement of aircraft over the long-term. A number of flights, each with a requirement for a specific number and type of aircraft, are already scheduled over a long horizon. We need to assign aircraft to flights and schedule repair activities while considering the flights requirements, repair capacity, and aircraft failures. The number of aircraft awaiting repair dynamically changes over time due to failures and it is therefore necessary to rebuild the repair schedule online. To solve the problem, we view the dynamic repair shop as successive static repair scheduling sub-problems over shorter time periods. We propose a complete approach based on the logic-based Benders decomposition to solve the static sub-problems, and design different rescheduling policies to schedule the dynamic repair shop. Computational experiments demonstrate that the Benders model is able to find and prove optimal solutions on average four times faster than a mixed integer programming model. The rescheduling approach having both aspects of scheduling over a longer horizon and quickly adjusting the schedule increases aircraft available in the long term by 10% compared to the approaches having either one of the aspects alone.

A computer program for simulating time travel and a possible 'solution' for the grandfather paradox

While the possibility of time travel in physics is still debated, the explosive growth of virtual-reality simulations opens up new possibilities to rigorously explore such time travel and its consequences in the digital domain. Here we provide a computational model of time travel and a computer program that allows exploring digital time travel. In order to explain our method we formalize a simplified version of the famous grandfather paradox, show how the system can allow the participant to go back in time, try to kill their ancestors before they were born, and experience the consequences. The system has even come up with scenarios that can be considered consistent "solutions" of the grandfather paradox. We discuss the conditions for digital time travel, which indicate that it has a large number of practical applications.

Detection Algorithms for Communication Systems Using Deep Learning

The design and analysis of communication systems typically rely on the development of mathematical models that describe the underlying communication channel, which dictates the relationship between the transmitted and the received signals. However, in some systems, such as molecular communication systems where chemical signals are used for transfer of information, it is not possible to accurately model this relationship. In these scenarios, because of the lack of mathematical channel models, a completely new approach to design and analysis is required. In this work, we focus on one important aspect of communication systems, the detection algorithms, and demonstrate that by borrowing tools from deep learning, it is possible to train detectors that perform well, without any knowledge of the underlying channel models. We evaluate these algorithms using experimental data that is collected by a chemical communication platform, where the channel model is unknown and difficult to model analytically. We show that deep learning algorithms perform significantly better than a simple detector that was used in previous works, which also did not assume any knowledge of the channel.

On the energy landscape of deep networks

We study a theoretical model that connects deep learning to finding the ground state of the Hamiltonian of a spherical spin glass. Existing results motivated from statistical physics show that deep networks have a highly non-convex energy landscape with exponentially many local minima and energy barriers beyond which gradient descent algorithms cannot make progress. We leverage a technique known as topology trivialization where, upon perturbation by an external magnetic field, the energy landscape of the spin glass Hamiltonian changes dramatically from exponentially many local minima to "total trivialization", i.e., a constant number of local minima. There also exists a transitional regime with polynomially many local minima which interpolates between these extremes. We show that a number of regularization schemes in deep learning can benefit from this phenomenon. As a consequence, our analysis provides order heuristics to choose regularization parameters and motivates annealing schemes for these perturbations.

(Probably) Concave Graph Matching

In this paper we address the graph matching problem. Following the recent works of \cite{zaslavskiy2009path,Vestner2017} we analyze and generalize the idea of concave relaxations. We introduce the concepts of \emph{conditionally concave} and \emph{probably conditionally concave} energies on polytopes and show that they encapsulate many instances of the graph matching problem, including matching Euclidean graphs and graphs on surfaces. We further prove that local minima of probably conditionally concave energies on general matching polytopes (\eg, doubly stochastic) are with high probability extreme points of the matching polytope (\eg, permutations).

Ultradense Word Embeddings by Orthogonal Transformation

Embeddings are generic representations that are useful for many NLP tasks. In this paper, we introduce DENSIFIER, a method that learns an orthogonal transformation of the embedding space that focuses the information relevant for a task in an ultradense subspace of a dimensionality that is smaller by a factor of 100 than the original space. We show that ultradense embeddings generated by DENSIFIER reach state of the art on a lexicon creation task in which words are annotated with three types of lexical information - sentiment, concreteness and frequency. On the SemEval2015 10B sentiment analysis task we show that no information is lost when the ultradense subspace is used, but training is an order of magnitude more efficient due to the compactness of the ultradense space.

Ancestral Causal Inference

Constraint-based causal discovery from limited data is a notoriously difficult challenge due to the many borderline independence test decisions. Several approaches to improve the reliability of the predictions by exploiting redundancy in the independence information have been proposed recently. Though promising, existing approaches can still be greatly improved in terms of accuracy and scalability. We present a novel method that reduces the combinatorial explosion of the search space by using a more coarse-grained representation of causal information, drastically reducing computation time. Additionally, we propose a method to score causal predictions based on their confidence. Crucially, our implementation also allows one to easily combine observational and interventional data and to incorporate various types of available background knowledge. We prove soundness and asymptotic consistency of our method and demonstrate that it can outperform the state-of-the-art on synthetic data, achieving a speedup of several orders of magnitude. We illustrate its practical feasibility by applying it on a challenging protein data set.

Learning Disjunctions of Predicates

Let $F$ be a set of boolean functions. We present an algorithm for learning $F_\vee := \{\vee_{f\in S} f \mid S \subseteq F\}$ from membership queries. Our algorithm asks at most $|F| \cdot OPT(F_\vee)$ membership queries where $OPT(F_\vee)$ is the minimum worst case number of membership queries for learning $F_\vee$. When $F$ is a set of halfspaces over a constant dimension space or a set of variable inequalities, our algorithm runs in polynomial time.

A Novel Online Real-time Classifier for Multi-label Data Streams

In this paper, a novel extreme learning machine based online multi-label classifier for real-time data streams is proposed. Multi-label classification is one of the actively researched machine learning paradigm that has gained much attention in the recent years due to its rapidly increasing real world applications. In contrast to traditional binary and multi-class classification, multi-label classification involves association of each of the input samples with a set of target labels simultaneously. There are no real-time online neural network based multi-label classifier available in the literature. In this paper, we exploit the inherent nature of high speed exhibited by the extreme learning machines to develop a novel online real-time classifier for multi-label data streams. The developed classifier is experimented with datasets from different application domains for consistency, performance and speed. The experimental studies show that the proposed method outperforms the existing state-of-the-art techniques in terms of speed and accuracy and can classify multi-label data streams in real-time.

ESmodels: An Epistemic Specification Solver

(To appear in Theory and Practice of Logic Programming (TPLP))

The Convexity and Design of Composite Multiclass Losses

We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore the implications. We also show how the separation of concerns afforded by using this composite representation allows for the design of families of losses with the same Bayes risk.

Hierarchical Optimal Transport for Document Representation

The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora. Past distances between documents suffer from either an inability to incorporate semantic similarities between words or from scalability issues. As an alternative, we introduce hierarchical optimal transport as a meta-distance between documents, where documents are modeled as distributions over topics, which themselves are modeled as distributions over words. We then solve an optimal transport problem on the smaller topic space to compute a similarity score. We give conditions on the topics under which this construction defines a distance, and we relate it to the word mover's distance. We evaluate our technique for k-NN classification and show better interpretability and scalability with comparable performance to current methods at a fraction of the cost.

A Synaptical Story of Persistent Activity with Graded Lifetime in a Neural System

Persistent activity refers to the phenomenon that cortical neurons keep firing even after the stimulus triggering the initial neuronal responses is moved. Persistent activity is widely believed to be the substrate for a neural system retaining a memory trace of the stimulus information. In a conventional view, persistent activity is regarded as an attractor of the network dynamics, but it faces a challenge of how to be closed properly. Here, in contrast to the view of attractor, we consider that the stimulus information is encoded in a marginally unstable state of the network which decays very slowly and exhibits persistent firing for a prolonged duration. We propose a simple yet effective mechanism to achieve this goal, which utilizes the property of short-term plasticity (STP) of neuronal synapses. STP has two forms, short-term depression (STD) and short-term facilitation (STF), which have opposite effects on retaining neuronal responses. We find that by properly combining STF and STD, a neural system can hold persistent activity of graded lifetime, and that persistent activity fades away naturally without relying on an external drive. The implications of these results on neural information representation are discussed.

ResNets Ensemble via the Feynman-Kac Formalism to Improve Natural and Robust Accuracies

We unify the theory of optimal control of transport equations with the practice of training and testing of ResNets. Based on this unified viewpoint, we propose a simple yet effective ResNets ensemble algorithm to boost the accuracy of the robustly trained model on both clean and adversarial images. The proposed algorithm consists of two components: First, we modify the base ResNets by injecting a variance specified Gaussian noise to the output of each residual mapping. Second, we average over the production of multiple jointly trained modified ResNets to get the final prediction. These two steps give an approximation to the Feynman-Kac formula for representing the solution of a convection-diffusion equation. For the CIFAR10 benchmark, this simple algorithm leads to a robust model with a natural accuracy of {\bf 85.62}\% on clean images and a robust accuracy of ${\bf 57.94 \%}$ under the 20 iterations of the IFGSM attack, which outperforms the current state-of-the-art in defending against IFGSM attack on the CIFAR10.

Semi-supervised Data Representation via Affinity Graph Learning

We consider the general problem of utilizing both labeled and unlabeled data to improve data representation performance. A new semi-supervised learning framework is proposed by combing manifold regularization and data representation methods such as Non negative matrix factorization and sparse coding. We adopt unsupervised data representation methods as the learning machines because they do not depend on the labeled data, which can improve machine's generation ability as much as possible. The proposed framework forms the Laplacian regularizer through learning the affinity graph. We incorporate the new Laplacian regularizer into the unsupervised data representation to smooth the low dimensional representation of data and make use of label information. Experimental results on several real benchmark datasets indicate that our semi-supervised learning framework achieves encouraging results compared with state-of-art methods.

Third-order Smoothness Helps: Faster Stochastic Optimization Algorithms for Finding Local Minima

We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently. More specifically, the proposed algorithm only needs $\tilde{O}(\epsilon^{-10/3})$ stochastic gradient evaluations to converge to an approximate local minimum $\mathbf{x}$, which satisfies $\|\nabla f(\mathbf{x})\|_2\leq\epsilon$ and $\lambda_{\min}(\nabla^2 f(\mathbf{x}))\geq -\sqrt{\epsilon}$ in unconstrained stochastic optimization, where $\tilde{O}(\cdot)$ hides logarithm polynomial terms and constants. This improves upon the $\tilde{O}(\epsilon^{-7/2})$ gradient complexity achieved by the state-of-the-art stochastic local minima finding algorithms by a factor of $\tilde{O}(\epsilon^{-1/6})$. Experiments on two nonconvex optimization problems demonstrate the effectiveness of our algorithm and corroborate our theory.

Chess Game Concepts Emerge under Weak Supervision: A Case Study of Tic-tac-toe

This paper explores the possibility of learning chess game concepts under weak supervision with convolutional neural networks, which is a topic that has not been visited to the best of our knowledge. We put this task in three different backgrounds: (1) deep reinforcement learning has shown an amazing capability to learn a mapping from visual inputs to most rewarding actions, without knowing the concepts of a video game. But how could we confirm that the network understands these concepts or it just does not? (2) cross-modal supervision for visual representation learning draws much attention recently. Is this methodology still applicable when it comes to the domain of game concepts and actions? (3) class activation mapping is widely recognized as a visualization technique to help us understand what a network has learnt. Is it possible for it to activate at non-salient regions? With the simplest chess game tic-tac-toe, we report interesting results as answers to those three questions mentioned above. All codes, pre-processed datasets and pre-trained models will be released.

Argumentation Semantics for Prioritised Default Logic

We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions. Argumentation semantics for PDL will allow for the application of argument game proof theories to the process of inference in PDL, making the reasons for accepting a conclusion transparent and the inference process more intuitive. This also opens up the possibility for argumentation-based distributed reasoning and communication amongst agents with PDL representations of mental attitudes.

A Unified Framework for Data Poisoning Attack to Graph-based Semi-supervised Learning

In this paper, we proposed a general framework for data poisoning attacks to graph-based semi-supervised learning (G-SSL). In this framework, we first unify different tasks, goals and constraints into a single formula for data poisoning attack in G-SSL, then we propose two specialized algorithms to efficiently solve two important cases --- poisoning regression tasks under $\ell_2$-norm constraint and classification tasks under $\ell_0$-norm constraint. In the former case, we transform it into a non-convex trust region problem and show that our gradient-based algorithm with delicate initialization and update scheme finds the (globally) optimal perturbation. For the latter case, although it is an NP-hard integer programming problem, we propose a probabilistic solver that works much better than the classical greedy method. Lastly, we test our framework on real datasets and evaluate the robustness of G-SSL algorithms. For instance, on the MNIST binary classification problem (50000 training data with 50 labeled), flipping two labeled data is enough to make the model perform like random guess (around 50\% error).

Temporal Attention-Gated Model for Robust Sequence Classification

Typical techniques for sequence classification are designed for well-segmented sequences which has been edited to remove noisy or irrelevant parts. Therefore, such methods cannot be easily applied on noisy sequences which are expected in real-world applications. We present the Temporal Attention-Gated Model (TAGM) which is able to deal with noisy sequences. Our model assimilates ideas from attention models and gated recurrent networks. Specifically, we employ an attention model to measure the relevance of each time step of a sequence to the final decision. We then use the relevant segments based on their attention scores in a novel gated recurrent network to learn the hidden representation for the classification. More importantly, our attention weights provide a physically meaningful interpretation for the salience of each time step in the sequence. We demonstrate the merits of our model in both interpretability and classification performance on a variety of tasks, including speech recognition, textual sentiment analysis and event recognition.

Regularized EM Algorithms: A Unified Framework and Statistical Guarantees

Latent models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet our rigorous understanding of its performance is highly incomplete. Recently, work in [1] has demonstrated that for an important class of problems, EM exhibits linear local convergence. In the high-dimensional setting, however, the M-step may not be well defined. We address precisely this setting through a unified treatment using regularization. While regularization for high-dimensional problems is by now well understood, the iterative EM algorithm requires a careful balancing of making progress towards the solution while identifying the right structure (e.g., sparsity or low-rank). In particular, regularizing the M-step using the state-of-the-art high-dimensional prescriptions (e.g., `a la [19]) is not guaranteed to provide this balance. Our algorithm and analysis are linked in a way that reveals the balance between optimization and statistical errors. We specialize our general framework to sparse gaussian mixture models, high-dimensional mixed regression, and regression with missing variables, obtaining statistical guarantees for each of these examples.

Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation

We present a new algorithm, truncated variance reduction (TruVaR), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a set of potential maximizers (BO) or unclassified points (LSE), which is updated based on confidence bounds. TruVaR is effective in several important settings that are typically non-trivial to incorporate into myopic algorithms, including pointwise costs and heteroscedastic noise. We provide a general theoretical guarantee for TruVaR covering these aspects, and use it to recover and strengthen existing results on BO and LSE. Moreover, we provide a new result for a setting where one can select from a number of noise levels having associated costs. We demonstrate the effectiveness of the algorithm on both synthetic and real-world data sets.

Using MathML to Represent Units of Measurement for Improved Ontology Alignment

Ontologies provide a formal description of concepts and their relationships in a knowledge domain. The goal of ontology alignment is to identify semantically matching concepts and relationships across independently developed ontologies that purport to describe the same knowledge. In order to handle the widest possible class of ontologies, many alignment algorithms rely on terminological and structural meth- ods, but the often fuzzy nature of concepts complicates the matching process. However, one area that should provide clear matching solutions due to its mathematical nature, is units of measurement. Several on- tologies for units of measurement are available, but there has been no attempt to align them, notwithstanding the obvious importance for tech- nical interoperability. We propose a general strategy to map these (and similar) ontologies by introducing MathML to accurately capture the semantic description of concepts specified therein. We provide mapping results for three ontologies, and show that our approach improves on lexical comparisons.

Glow: Generative Flow with Invertible 1x1 Convolutions

Flow-based generative models are conceptually attractive due to tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis. In this paper we propose Glow, a simple type of generative flow using invertible 1x1 convolution. Using our method we demonstrate a significant improvement in log-likelihood and qualitative sample quality. Perhaps most strikingly, we demonstrate that a generative model optimized towards the plain log-likelihood objective is capable of efficient synthesis of large and subjectively realistic-looking images.

Near Optimal Behavior via Approximate State Abstraction

The combinatorial explosion that plagues planning and reinforcement learning (RL) algorithms can be moderated using state abstraction. Prohibitively large task representations can be condensed such that essential information is preserved, and consequently, solutions are tractably computable. However, exact abstractions, which treat only fully-identical situations as equivalent, fail to present opportunities for abstraction in environments where no two situations are exactly alike. In this work, we investigate approximate state abstractions, which treat nearly-identical situations as equivalent. We present theoretical guarantees of the quality of behaviors derived from four types of approximate abstractions. Additionally, we empirically demonstrate that approximate abstractions lead to reduction in task complexity and bounded loss of optimality of behavior in a variety of environments.

Neural Domain Adaptation for Biomedical Question Answering

Factoid question answering (QA) has recently benefited from the development of deep learning (DL) systems. Neural network models outperform traditional approaches in domains where large datasets exist, such as SQuAD (ca. 100,000 questions) for Wikipedia articles. However, these systems have not yet been applied to QA in more specific domains, such as biomedicine, because datasets are generally too small to train a DL system from scratch. For example, the BioASQ dataset for biomedical QA comprises less then 900 factoid (single answer) and list (multiple answers) QA instances. In this work, we adapt a neural QA system trained on a large open-domain dataset (SQuAD, source) to a biomedical dataset (BioASQ, target) by employing various transfer learning techniques. Our network architecture is based on a state-of-the-art QA system, extended with biomedical word embeddings and a novel mechanism to answer list questions. In contrast to existing biomedical QA systems, our system does not rely on domain-specific ontologies, parsers or entity taggers, which are expensive to create. Despite this fact, our systems achieve state-of-the-art results on factoid questions and competitive results on list questions.

On Approximate Dynamic Programming with Multivariate Splines for Adaptive Control

We define a SDP framework based on the RLSTD algorithm and multivariate simplex B-splines. We introduce a local forget factor capable of preserving the continuity of the simplex splines. This local forget factor is integrated with the RLSTD algorithm, resulting in a modified RLSTD algorithm that is capable of tracking time-varying systems. We present the results of two numerical experiments, one validating SDP and comparing it with NDP and another to show the advantages of the modified RLSTD algorithm over the original. While SDP requires more computations per time-step, the experiment shows that for the same amount of function approximator parameters, there is an increase in performance in terms of stability and learning rate compared to NDP. The second experiment shows that SDP in combination with the modified RLSTD algorithm allows for faster recovery compared to the original RLSTD algorithm when system parameters are altered, paving the way for an adaptive high-performance non-linear control method.

Gated Neural Networks for Option Pricing: Rationality by Design

We propose a neural network approach to price EU call options that significantly outperforms some existing pricing models and comes with guarantees that its predictions are economically reasonable. To achieve this, we introduce a class of gated neural networks that automatically learn to divide-and-conquer the problem space for robust and accurate pricing. We then derive instantiations of these networks that are 'rational by design' in terms of naturally encoding a valid call option surface that enforces no arbitrage principles. This integration of human insight within data-driven learning provides significantly better generalisation in pricing performance due to the encoded inductive bias in the learning, guarantees sanity in the model's predictions, and provides econometrically useful byproduct such as risk neutral density.

Comparison three methods of clustering: k-means, spectral clustering and hierarchical clustering

Comparison of three kind of the clustering and find cost function and loss function and calculate them. Error rate of the clustering methods and how to calculate the error percentage always be one on the important factor for evaluating the clustering methods, so this paper introduce one way to calculate the error rate of clustering methods. Clustering algorithms can be divided into several categories including partitioning clustering algorithms, hierarchical algorithms and density based algorithms. Generally speaking we should compare clustering algorithms by Scalability, Ability to work with different attribute, Clusters formed by conventional, Having minimal knowledge of the computer to recognize the input parameters, Classes for dealing with noise and extra deposition that same error rate for clustering a new data, Thus, there is no effect on the input data, different dimensions of high levels, K-means is one of the simplest approach to clustering that clustering is an unsupervised problem.

Communications Inspired Linear Discriminant Analysis

We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label (based on a Shannon entropy measure). By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent, without requiring simplification of the objective function. Theoretical analysis and empirical comparison are made between the proposed method and two closely related methods (Linear Discriminant Analysis and Information Discriminant Analysis), and comparisons are also made with a method in which Renyi entropy is used to define the mutual information (in this case the gradient may be computed simply, under a special parameter setting). Relative to these alternative approaches, the proposed method achieves promising results on real datasets.

Generalized Sliced Wasserstein Distances

The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community. The SW distance, specifically, was shown to have similar properties to the Wasserstein distance, while being much simpler to compute, and is therefore used in various applications including generative modeling and general supervised/unsupervised learning. In this paper, we first clarify the mathematical connection between the SW distance and the Radon transform. We then utilize the generalized Radon transform to define a new family of distances for probability measures, which we call generalized sliced-Wasserstein (GSW) distances. We further show that, similar to the SW distance, the GSW distance can be extended to a maximum GSW (max-GSW) distance. We then provide the conditions under which GSW and max-GSW distances are indeed proper metrics. Finally, we compare the numerical performance of the proposed distances on the generative modeling task of SW flows and report favorable results.