In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates. To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a loss function enjoying suitable robustness properties. In this paper, we build a pseudo-likelihood based on the Maximum Mean Discrepancy, defined via an embedding of probability distributions into a reproducing kernel Hilbert space. We show that this MMD-Bayes posterior is consistent and robust to model misspecification. As the posterior obtained in this way might be intractable, we also prove that reasonable variational approximations of this posterior enjoy the same properties. We provide details on a stochastic gradient algorithm to compute these variational approximations. Numerical simulations indeed suggest that our estimator is more robust to misspecification than the ones based on the likelihood. Keywords: Maximum Mean Discrepancy, Robust estimation, Variational inference.

Predicting the next position of movable objects has been a problem for at least the last three decades, referred to as trajectory prediction. In our days, the vast amounts of data being continuously produced add the big data dimension to the trajectory prediction problem, which we are trying to tackle by creating a {\lambda}-Architecture based analytics platform. This platform performs both batch and stream analytics tasks and then combines them to perform analytical tasks that cannot be performed by analyzing any of these layers by itself. The biggest benefit of this platform is its context agnostic trait, which allows us to use it for any use case, as long as a time-stamped geolocation stream is provided. The experimental results presented prove that each part of the {\lambda}-Architecture performs well at certain targets, making a combination of these parts a necessity in order to improve the overall accuracy and performance of the platform.

Learning to align multiple datasets is an important problem with many applications, and it is especially useful when we need to integrate multiple experiments or correct for confounding. Optimal transport (OT) is a principled approach to align datasets, but a key challenge in applying OT is that we need to specify a transport cost function that accurately captures how the two datasets are related. Reliable cost functions are typically not available and practitioners often resort to using hand-crafted or Euclidean cost even if it may not be appropriate. In this work, we investigate how to learn the cost function using a small amount of side information which is often available. The side information we consider captures subset correspondence---i.e. certain subsets of points in the two data sets are known to be related. For example, we may have some images labeled as cars in both datasets; or we may have a common annotated cell type in single-cell data from two batches. We develop an end-to-end optimizer (OT-SI) that differentiates through the Sinkhorn algorithm and effectively learns the suitable cost function from side information. On systematic experiments in images, marriage-matching and single-cell RNA-seq, our method substantially outperform state-of-the-art benchmarks.

We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighborhood relationships over multiple scales is useful for a diverse range of applications, including latent feature identification across disconnected networks with similar attributes. We prove theoretically that matrices of node-feature pointwise mutual information are implicitly factorized by the embeddings. Experiments show that our algorithms are robust, computationally efficient and outperform comparable models on social, web and citation network datasets. Node embedding is a fundamental technique in network analysis that serves as a precursor to numerous downstream machine learning and optimisation tasks, e.g. Several recent network embedding methods, such as Deepwalk (Perozzi et al., 2014), Node2V ec(Grover & Leskovec, 2016) and W alklets(Perozzi et al., 2017), achieve impressive performance by learning the network structure following an approach similar to W ord2V ec Skip-gram(Mikolov et al., 2013b), originally designed for word embedding. In these works, sequences of neighboring nodes are generated from random walks over a network, and representations are distilled from extracted node-node proximity statistics that capture local neighbourhood information. When the nodes of a network have attributes (or features), their embeddings can be used to capture information about the attributes in their local neighbourhood. For a social network, attributes might represent a person's interests, habits, history or preferences. The pattern of node attributes are often similar in a neighborhood, and conversely, nodes with similar attributes are more likely to be connected. This property is known as homophily.

This paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as "this is better than that" between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. The surrogate is fit by means of radial basis functions, under the constraint of satisfying, if possible, the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is superior in that, within the same number of comparisons, it approaches the global optimum more closely and is computationally lighter. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/idwgopt.

Kleinberg [2] coined the term of k -richness of distance-based clustering algorithms, meaning the possibility to partition a set of objects into any k nonempty (disjoint) subsets via modifying the distances between these obje cts. However, there exist non-deterministic, probabilistic algorithms which do not fi t this characterization because of non-deterministic behaviour. Therefore Ackerman at el [1, Definition 3 ( k -Richness)] introduce the concept of probabilistic k -richness. This kind of richness they defined as Property 1. For any partition Γ of the set X consisting of exactly k clusters and every ǫ 0 there exists such a distance function d that the clustering function returns this partition Γ with probability exceeding 1 ǫ . They postulate in their Fig.2 (omitting the proof) that probabilistic k -richness in probabilistic sense is possessed by version of the k -means

It is always an attractive task to discover knowledge for various learning problems; however, this knowledge discovery and maintenance process usually suffers from noise, incompleteness or knowledge domain mismatch. Thus, robust knowledge discovery by removing the noisy features or samples, complementing incomplete data, and mitigating the distribution difference becomes the key. Along this line of research, low-rank modeling is widely-used to solve these challenges. This survey covers the topic of: (1) robust knowledge recovery, (2) robust knowledge transfer, (3) robust knowledge fusion, centered around several major applications. First of all, we deliver a unified formulation for robust knowledge discovery based on a given dataset. Second, we discuss robust knowledge transfer and fusion given multiple datasets with different knowledge flows, followed by practical challenges, model variations, and remarks. Finally, we highlight future research of robust knowledge discovery for incomplete, unbalance, large-scale data analysis. This would benefit AI community from literature review to future direction.

Deep neural networks (DNNs) are known for extracting good representations from a large amount of data. However, the representations learned in DNNs are typically hard to interpret, especially the ones learned in dense layers. One crucial issue is that neurons within each layer of DNNs are conditionally independent with each other, which makes the co-training and analysis of neurons at higher modularity difficult. In contrast, the dependency patterns of biological neurons in the human brain are largely different from those of DNNs. Neuronal assembly describes such neuron dependencies that could be found among a group of biological neurons as having strong internal synaptic interactions, potentially high semantical correlations that are deemed to facilitate the memorization process. In this paper, we show such a crucial gap between DNNs and biological neural networks (BNNs) can be bridged by the newly proposed Biologically-Enhanced Artificial Neuronal assembly (BEAN) regularization that could enforce dependencies among neurons in dense layers of DNNs without altering the conventional architecture. Both qualitative and quantitative analyses show that BEAN enables the formations of interpretable and biologically plausible neuronal assemblies in dense layers and consequently enhances the modularity and interpretability of the hidden representations learned. Moreover, BEAN further results in sparse and structured connectivity and parameter sharing among neurons, which substantially improves the efficiency and generalizability of the model.

The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of challenges especially when analyzing high-dimensional data sets in which the number of predictors $\mathit{p}$ is much larger than number of samples $n,~(n\ll p)$. A new covariance estimator, called the \textit{Maximum Entropy Covariance} (MEC) that addresses loss of covariance information when similar covariance matrices are linearly combined using \textit{Maximum Entropy} (ME) principle is proposed in this work. By benefitting naturally from slicing or discretizing range of the response variable, y into \textit{H} non-overlapping categories, $\mathit{h_{1},\ldots ,h_{H}}$, MEC first combines covariance matrices arising from samples in each y slice $\mathit{h\in H}$ and then select the one that maximizes entropy under the principle of maximum uncertainty. The MEC estimator is then formed from convex mixture of such entropy-maximizing sample covariance $S_{\mbox{mec}}$ estimate and pooled sample covariance $\mathbf{S}_{\mathit{p}}$ estimate across the $\mathit{H}$ slices without requiring time-consuming covariance optimization procedures. MEC deals directly with singularity and instability of sample group covariance estimate in both regression and classification problems. The efficiency of the MEC estimator is studied with the existing sufficient dimension reduction methods such as \textit{Sliced Inverse Regression} (SIR) and \textit{Sliced Average Variance Estimator} (SAVE) as demonstrated on both classification and regression problems using real life Leukemia cancer data and customers' electricity load profiles from smart meter data sets respectively.

News items have a significant impact on stock markets but the ways are obscure. Many previous works have aimed at finding accurate stock market forecasting models. In this paper, we use text mining and sentiment analysis on Chinese online financial news, to predict Chinese stock tendency and stock prices based on support vector machine (SVM). Firstly, we collect 2,302,692 news items, which date from 1/1/2008 to 1/1/2015. Secondly, based on this dataset, a specific domain stop-word dictionary and a precise sentiment dictionary are formed. Thirdly, we propose a forecasting model using SVM. On the algorithm of SVM implementation, we also propose two-parameter optimization algorithms to search for the best initial parameter setting. The result shows that parameter G has the main effect, while parameter C's effect is not obvious. Furthermore, support vector regression (SVR) models for different Chinese stocks are similar whereas in support vector classification (SVC) models best parameters are quite differential. Series of contrast experiments show that: a) News has significant influence on stock market; b) Expansion input vector for additional situations when that day has no news data is better than normal input in SVR, yet is worse in SVC; c) SVR shows a fantastic degree of fitting in predicting stock fluctuation while such result has some time lag; d) News effect time lag for stock market is less than two days; e) In SVC, historic stock data has a most efficient time lag which is about 10 days, whereas in SVR this effect is not obvious. Besides, based on the special structure of the input vector, we also design a method to calculate the financial source impact factor. Result suggests that the news quality and audience number both have a significant effect on the source impact factor. Besides, for Chinese investors, traditional media has more influence than digital media.