This paper proposes adaptive fractional order graph neural network (AFGNN), optimized by a time-varying fractional order gradient descent method to address the challenges of local optimum of classic and fractional GNNs which are specialised at aggregating information from the feature and adjacent matrices of connected nodes and their neighbours to solve learning tasks on non-Euclidean data such as graphs. To overcome the high computational complexity of fractional order derivations, the proposed model approximately calculates the fractional order gradients. We further prove such approximation is feasible and the AFGNN is unbiased. Extensive experiments on benchmark citation networks and object recognition challenges confirm the performance of AFGNN. The first group of experiments show that the results of AFGNN outperform the steepest gradient based method and conventional GNNs on the citation networks.

With the explosion of massive, widely available unlabeled data in the past years, finding label and time efficient, robust learning algorithms has become ever more important in theory and in practice. We study the paradigm of active learning, in which algorithms with access to large pools of data may adaptively choose what samples to label in the hope of exponentially increasing efficiency. By introducing comparisons, an additional type of query comparing two points, we provide the first time and query efficient algorithms for learning non-homogeneous linear separators robust to bounded (Massart) noise. We further provide algorithms for a generalization of the popular Tsybakov low noise condition, and show how comparisons provide a strong reliability guarantee that is often impractical or impossible with only labels - returning a classifier that makes no errors with high probability.

We consider the fundamental problem of learning a single neuron $x \mapsto\sigma(w^\top x)$ using standard gradient methods. As opposed to previous works, which considered specific (and not always realistic) input distributions and activation functions $\sigma(\cdot)$, we ask whether a more general result is attainable, under milder assumptions. On the one hand, we show that some assumptions on the distribution and the activation function are necessary. On the other hand, we prove positive guarantees under mild assumptions, which go beyond those studied in the literature so far. We also point out and study the challenges in further strengthening and generalizing our results.

We study computational aspects of relational marginal polytopes which are statistical relational learning counterparts of marginal polytopes, well-known from probabilistic graphical models. Here, given some first-order logic formula, we can define its relational marginal statistic to be the fraction of groundings that make this formula true in a given possible world. For a list of first-order logic formulas, the relational marginal polytope is the set of all points that correspond to the expected values of the relational marginal statistics that are realizable. In this paper, we study the following two problems: (i) Do domain-liftability results for the partition functions of Markov logic networks (MLNs) carry over to the problem of relational marginal polytope construction? (ii) Is the relational marginal polytope containment problem hard under some plausible complexity-theoretic assumptions? Our positive results have consequences for lifted weight learning of MLNs. In particular, we show that weight learning of MLNs is domain-liftable whenever the computation of the partition function of the respective MLNs is domain-liftable (this result has not been rigorously proven before).

Information extracted from electrohysterography recordings could potentially prove to be an interesting additional source of information to estimate the risk on preterm birth. Recently, a large number of studies have reported near-perfect results to distinguish between recordings of patients that will deliver term or preterm using a public resource, called the Term/Preterm Electrohysterogram database. However, we argue that these results are overly optimistic due to a methodological flaw being made. In this work, we focus on one specific type of methodological flaw: applying oversampling before partitioning the data into mutually exclusive training and testing sets. We show how this causes the results to be biased using two artificial datasets and reproduce results of studies in which this flaw was identified. Moreover, we evaluate the actual impact of oversampling on predictive performance, when applied prior to data partitioning, using the same methodologies of related studies, to provide a realistic view of these methodologies' generalization capabilities. We make our research reproducible by providing all the code under an open license. Keywords: preterm birth risk estimation · oversampling · electrohysterogra-phy 1 Introduction Giving birth before 37 weeks of pregnancy, which is referred to as preterm birth, has a significant negative impact on the expected outcome of the neonate. According to the World Health Organization (WHO), preterm birth is one of the arXiv:2001.06296v1

Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used models like the Dirichlet process and the beta-Bernoulli process can be expressed as, are decomposable into independent sub-measures. We use this decomposition to partition the latent measure into a finite measure containing only in-stantiated components, and an infinite measure containing all other components. We then select different inference algorithms for the two components: uncollapsed samplers mix well on the finite measure, while collapsed samplers mix well on the infinite, sparsely occupied tail. The resulting hybrid algorithm can be applied to a wide class of models, and can be easily distributed to allow scalable inference without sacrificing asymptotic convergence guarantees.

Single-site Markov Chain Monte Carlo (MCMC) is a variant of MCMC in which a single coordinate in the state space is modified in each step. Structured relational models are a good candidate for this style of inference. In the single-site context, second order methods become feasible because the typical cubic costs associated with these methods is now restricted to the dimension of each coordinate. Our work, which we call Newtonian Monte Carlo (NMC), is a method to improve MCMC convergence by analyzing the first and second order gradients of the target density to determine a suitable proposal density at each point. Existing first order gradient-based methods suffer from the problem of determining an appropriate step size. Too small a step size and it will take a large number of steps to converge, while a very large step size will cause it to overshoot the high density region. NMC is similar to the Newton-Raphson update in optimization where the second order gradient is used to automatically scale the step size in each dimension. However, our objective is to find a parameterized proposal density rather than the maxima. As a further improvement on existing first and second order methods, we show that random variables with constrained supports don't need to be transformed before taking a gradient step. We demonstrate the efficiency of NMC on a number of different domains. For statistical models where the prior is conjugate to the likelihood, our method recovers the posterior quite trivially in one step. However, we also show results on fairly large non-conjugate models, where NMC performs better than adaptive first order methods such as NUTS or other inexact scalable inference methods such as Stochastic Variational Inference or bootstrapping.

Dual averaging-type methods are widely used in industrial machine learning applications due to their ability to promoting solution structure (e.g., sparsity) efficiently. In this paper, we propose a novel accelerated dual-averaging primal-dual algorithm for minimizing a composite convex function. We also derive a stochastic version of the proposed method which solves empirical risk minimization, and its advantages on handling sparse data are demonstrated both theoretically and empirically.

In this manuscript we analyze a data set containing information on children with Hodgkin Lymphoma (HL) enrolled on a clinical trial. Treatments received and survival status were collected together with other covariates such as demographics and clinical measurements. Our main task is to explore the potential of machine learning (ML) algorithms in a survival analysis context in order to improve over the Cox Proportional Hazard (CoxPH) model. We discuss the weaknesses of the CoxPH model we would like to improve upon and then we introduce multiple algorithms, from well-established ones to state-of-the-art models, that solve these issues. We then compare every model according to the concordance index and the brier score. Finally, we produce a series of recommendations, based on our experience, for practitioners that would like to benefit from the recent advances in artificial intelligence.

The imperfectness of data acquisition processes, however, presents several common yet critical challenges: (1) random noise: which reflects the uncertainty of the environment and/or the measurement processes; (2) outliers: which represent a sort of corruption that exhibits abnormal behavior; and (3) incomplete data, namely, we might only get to observe a fraction of the matrix entries. Low-rank matrix estimation algorithms aimed at addressing these challenges have been extensively studied under the umbrella of robust principal component analysis (Robust PCA) [CSPW11, CLMW11], a terminology popularized by the seminal work [CLMW11]. To formulate the above-mentioned problem in a more precise manner, imagine that we seek to estimate an unknown low-rank matrix L null R n n . 1 What we can obtain is a collection of partially observed and corrupted entries as follows M ij L null ij S null ij E ij, (i,j) Ω obs, (1.1) where S null [ S null ij] 1 i,j n is a matrix consisting of outliers, E [ E ij] 1 i,j n represents the random noise, and we only observe entries over an index subset Ω obs [n ] [n ] with [n ]: {1, 2, ···,n }. The current paper assumes that S null is a relatively sparse matrix whose nonzero entries might have arbitrary magnitudes. This assumption has been commonly adopted in prior work to model gross outliers, while enabling reliable disentanglement of the outlier component and the low-rank component [CSPW11,CLMW11,CJSC13,Li13]. In addition, we suppose that the entries {E ij} are independent zero-mean sub-Gaussian random variables, as commonly assumed in the statistics literature to model a large family of random noise. The aim is to reliably estimate L null given the grossly corrupted and possibly incomplete data (1.1). Ideally, this task should be accomplished without knowing the locations and magnitudes of the outliers S null . 1 To avoid cluttered notation, this paper works with square matrices of size n by n. Our results and analysis can be extended to accommodate rectangular matrices.