The widely applicable information criterion (WAIC) has been used as a model selection criterion for Bayesian statistics in recent years. It is an asymptotically unbiased estimator of the Kullback-Leibler divergence between a Bayesian predictive distribution and the true distribution. Not only is the WAIC theoretically more sound than other information criteria, its usefulness in practice has also been reported. On the other hand, the WAIC is intended for settings in which the prior distribution does not have an asymptotic influence, and as we set the class of the prior distribution to be more complex, it never fails to select the most complex one. To alleviate these concerns, this paper proposed the prior intensified information criterion (PIIC). In addition, it customizes this criterion to incorporate sparse estimation and causal inference. Numerical experiments show that the PIIC clearly outperforms the WAIC in terms of prediction performance when the above concerns are manifested. A real data analysis confirms that the results of variable selection and Bayesian estimators of the WAIC and PIIC differ significantly.
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We are interested in privatizing an approximate posterior inference algorithm called Expectation Propagation (EP). EP approximates the posterior by iteratively refining approximations to the local likelihoods, and is known to provide better posterior uncertainties than those by variational inference (VI). However, using EP for large-scale datasets imposes a challenge in terms of memory requirements as it needs to maintain each of the local approximates in memory. To overcome this problem, stochastic expectation propagation (SEP) was proposed, which only considers a unique local factor that captures the average effect of each likelihood term to the posterior and refines it in a way analogous to EP. In terms of privacy, SEP is more tractable than EP because at each refining step of a factor, the remaining factors are fixed to the same value and do not depend on other datapoints as in EP, which makes the sensitivity analysis tractable. We provide a theoretical analysis of the privacy-accuracy trade-off in the posterior estimates under differentially private stochastic expectation propagation (DP-SEP). Furthermore, we demonstrate the performance of our DP-SEP algorithm evaluated on both synthetic and real-world datasets in terms of the quality of posterior estimates at different levels of guaranteed privacy.
In recent decades, technological advances have made it possible to collect large data sets. In this context, the model-based clustering is a very popular, flexible and interpretable methodology for data exploration in a well-defined statistical framework. One of the ironies of the increase of large datasets is that missing values are more frequent. However, traditional ways (as discarding observations with missing values or imputation methods) are not designed for the clustering purpose. In addition, they rarely apply to the general case, though frequent in practice, of Missing Not At Random (MNAR) values, i.e. when the missingness depends on the unobserved data values and possibly on the observed data values. The goal of this paper is to propose a novel approach by embedding MNAR data directly within model-based clustering algorithms. We introduce a selection model for the joint distribution of data and missing-data indicator. It corresponds to a mixture model for the data distribution and a general MNAR model for the missing-data mechanism, which may depend on the underlying classes (unknown) and/or the values of the missing variables themselves. A large set of meaningful MNAR sub-models is derived and the identifiability of the parameters is studied for each of the sub-models, which is usually a key issue for any MNAR proposals. The EM and Stochastic EM algorithms are considered for estimation. Finally, we perform empirical evaluations for the proposed submodels on synthetic data and we illustrate the relevance of our method on a medical register, the TraumaBase (R) dataset.
Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide probabilistic uncertainty quantification in the sense of assigning beliefs to relevant assertions about the future observable. Alternatively, we recommend the use of a probabilistic predictor, a data-dependent (imprecise) probability distribution for the to-be-predicted observation given the observed data. It is essential that the probabilistic predictor be reliable or valid, and here we offer a notion of validity and explore its behavioral and statistical implications. In particular, we show that valid probabilistic predictors avoid sure loss and lead to prediction procedures with desirable frequentist error rate control properties. We also provide a general inferential model construction that yields a provably valid probabilistic predictor, and we illustrate this construction in regression and classification applications.
With the overwhelming popularity of Knowledge Graphs (KGs), researchers have poured attention to link prediction to fill in missing facts for a long time. However, they mainly focus on link prediction on binary relational data, where facts are usually represented as triples in the form of (head entity, relation, tail entity). In practice, n-ary relational facts are also ubiquitous. When encountering such facts, existing studies usually decompose them into triples by introducing a multitude of auxiliary virtual entities and additional triples. These conversions result in the complexity of carrying out link prediction on n-ary relational data. It has even proven that they may cause loss of structure information. To overcome these problems, in this paper, we represent each n-ary relational fact as a set of its role and role-value pairs. We then propose a method called NaLP to conduct link prediction on n-ary relational data, which explicitly models the relatedness of all the role and role-value pairs in an n-ary relational fact. We further extend NaLP by introducing type constraints of roles and role-values without any external type-specific supervision, and proposing a more reasonable negative sampling mechanism. Experimental results validate the effectiveness and merits of the proposed methods.
As data are increasingly being stored in different silos and societies becoming more aware of data privacy issues, the traditional centralized training of artificial intelligence (AI) models is facing efficiency and privacy challenges. Recently, federated learning (FL) has emerged as an alternative solution and continue to thrive in this new reality. Existing FL protocol design has been shown to be vulnerable to adversaries within or outside of the system, compromising data privacy and system robustness. Besides training powerful global models, it is of paramount importance to design FL systems that have privacy guarantees and are resistant to different types of adversaries. In this paper, we conduct the first comprehensive survey on this topic. Through a concise introduction to the concept of FL, and a unique taxonomy covering: 1) threat models; 2) poisoning attacks and defenses against robustness; 3) inference attacks and defenses against privacy, we provide an accessible review of this important topic. We highlight the intuitions, key techniques as well as fundamental assumptions adopted by various attacks and defenses. Finally, we discuss promising future research directions towards robust and privacy-preserving federated learning.
Click-through rate (CTR) prediction is one of the fundamental tasks for e-commerce search engines. As search becomes more personalized, it is necessary to capture the user interest from rich behavior data. Existing user behavior modeling algorithms develop different attention mechanisms to emphasize query-relevant behaviors and suppress irrelevant ones. Despite being extensively studied, these attentions still suffer from two limitations. First, conventional attentions mostly limit the attention field only to a single user's behaviors, which is not suitable in e-commerce where users often hunt for new demands that are irrelevant to any historical behaviors. Second, these attentions are usually biased towards frequent behaviors, which is unreasonable since high frequency does not necessarily indicate great importance. To tackle the two limitations, we propose a novel attention mechanism, termed Kalman Filtering Attention (KFAtt), that considers the weighted pooling in attention as a maximum a posteriori (MAP) estimation. By incorporating a priori, KFAtt resorts to global statistics when few user behaviors are relevant. Moreover, a frequency capping mechanism is incorporated to correct the bias towards frequent behaviors. Offline experiments on both benchmark and a 10 billion scale real production dataset, together with an Online A/B test, show that KFAtt outperforms all compared state-of-the-arts. KFAtt has been deployed in the ranking system of a leading e commerce website, serving the main traffic of hundreds of millions of active users everyday.
A new prior is proposed for learning representations of high-level concepts of the kind we manipulate with language. This prior can be combined with other priors in order to help disentangling abstract factors from each other. It is inspired by cognitive neuroscience theories of consciousness, seen as a bottleneck through which just a few elements, after having been selected by attention from a broader pool, are then broadcast and condition further processing, both in perception and decision-making. The set of recently selected elements one becomes aware of is seen as forming a low-dimensional conscious state. This conscious state is combining the few concepts constituting a conscious thought, i.e., what one is immediately conscious of at a particular moment. We claim that this architectural and information-processing constraint corresponds to assumptions about the joint distribution between high-level concepts. To the extent that these assumptions are generally true (and the form of natural language seems consistent with them), they can form a useful prior for representation learning. A low-dimensional thought or conscious state is analogous to a sentence: it involves only a few variables and yet can make a statement with very high probability of being true. This is consistent with a joint distribution (over high-level concepts) which has the form of a sparse factor graph, i.e., where the dependencies captured by each factor of the factor graph involve only very few variables while creating a strong dip in the overall energy function. The consciousness prior also makes it natural to map conscious states to natural language utterances or to express classical AI knowledge in a form similar to facts and rules, albeit capturing uncertainty as well as efficient search mechanisms implemented by attention mechanisms.
Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. For most applications, applying clustering is only appropriate when cluster structure is present. As such, the study of clusterability, which evaluates whether data possesses such structure, is an integral part of cluster analysis. However, methods for evaluating clusterability vary radically, making it challenging to select a suitable measure. In this paper, we perform an extensive comparison of measures of clusterability and provide guidelines that clustering users can reference to select suitable measures for their applications.
Machine Learning is a widely-used method for prediction generation. These predictions are more accurate when the model is trained on a larger dataset. On the other hand, the data is usually divided amongst different entities. For privacy reasons, the training can be done locally and then the model can be safely aggregated amongst the participants. However, if there are only two participants in \textit{Collaborative Learning}, the safe aggregation loses its power since the output of the training already contains much information about the participants. To resolve this issue, they must employ privacy-preserving mechanisms, which inevitably affect the accuracy of the model. In this paper, we model the training process as a two-player game where each player aims to achieve a higher accuracy while preserving its privacy. We introduce the notion of \textit{Price of Privacy}, a novel approach to measure the effect of privacy protection on the accuracy of the model. We develop a theoretical model for different player types, and we either find or prove the existence of a Nash Equilibrium with some assumptions. Moreover, we confirm these assumptions via a Recommendation Systems use case: for a specific learning algorithm, we apply three privacy-preserving mechanisms on two real-world datasets. Finally, as a complementary work for the designed game, we interpolate the relationship between privacy and accuracy for this use case and present three other methods to approximate it in a real-world scenario.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.
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