We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies does not match the prior distribution that the estimation method uses. These situations can arise from the positive definite requirement on correlation matrices, from the sign indeterminacy of factor loadings, and from order constraints on threshold parameters. The issue is especially problematic for reproducibility and for model checks that involve prior distributions, including prior predictive assessment and Bayes factors. In these cases, one might be assessing the wrong model, casting doubt on the relevance of the results. The most straightforward solution to these issues sometimes involves use of informative prior distributions. We explore other solutions and make recommendations for practice.
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As input data distributions evolve, the predictive performance of machine learning models tends to deteriorate. In practice, new input data tend to come without target labels. Then, state-of-the-art techniques model input data distributions or model prediction distributions and try to understand issues regarding the interactions between learned models and shifting distributions. We suggest a novel approach that models how explanation characteristics shift when affected by distribution shifts. We find that the modeling of explanation shifts can be a better indicator for detecting out-of-distribution model behaviour than state-of-the-art techniques. We analyze different types of distribution shifts using synthetic examples and real-world data sets. We provide an algorithmic method that allows us to inspect the interaction between data set features and learned models and compare them to the state-of-the-art. We release our methods in an open-source Python package, as well as the code used to reproduce our experiments.
Bayes factors for composite hypotheses have difficulty in encoding vague prior knowledge, as improper priors cannot be used and objective priors may be subjectively unreasonable. To address these issues we revisit the posterior Bayes factor, in which the posterior distribution from the data at hand is re-used in the Bayes factor for the same data. We argue that this is biased when calibrated against proper Bayes factors, but propose adjustments to allow interpretation on the same scale. In the important case of a regular normal model, the bias in log scale is half the number of parameters. The resulting empirical Bayes factor is closely related to the widely applicable information criterion. We develop test-based empirical Bayes factors for several standard tests and propose an extension to multiple testing closely related to the optimal discovery procedure. For non-parametric tests the empirical Bayes factor is approximately 10 times the P-value. We propose interpreting the strength of Bayes factors on a logarithmic scale with base 3.73, reflecting the sharpest distinction between weaker and stronger belief. This provides an objective framework for interpreting statistical evidence, realising a Bayesian/frequentist compromise.
Distributed statistical analyses provide a promising approach for privacy protection when analysing data distributed over several databases. It brings the analysis to the data and not the data to the analysis. The analyst receives anonymous summary statistics which are combined to a aggregated result. We are interested to calculate the AUC of a prediction score based on a distributed approach without getting to know the data of involved individual subjects distributed over different databases. We use DataSHIELD as the technology to carry out distributed analyses and use a newly developed algorithms to perform the validation of the prediction score. Calibration can easily be implemented in the distributed setting. But, discrimination represented by a respective ROC curve and its AUC is challenging. We base our approach on the ROC-GLM algorithm as well as on ideas of differential privacy. The proposed algorithms are evaluated in a simulation study. A real-word application is described: The audit use case of DIFUTURE (Medical Informatics Initiative) with the goal to validate a treatment prediction rule of patients with newly diagnosed multiple sclerosis.
Demonstrations provide insight into relevant state or action space regions, bearing great potential to boost the efficiency and practicality of reinforcement learning agents. In this work, we propose to leverage demonstration datasets by combining skill learning and sequence modeling. Starting with a learned joint latent space, we separately train a generative model of demonstration sequences and an accompanying low-level policy. The sequence model forms a latent space prior over plausible demonstration behaviors to accelerate learning of high-level policies. We show how to acquire such priors from state-only motion capture demonstrations and explore several methods for integrating them into policy learning on transfer tasks. Our experimental results confirm that latent space priors provide significant gains in learning speed and final performance. We benchmark our approach on a set of challenging sparse-reward environments with a complex, simulated humanoid, and on offline RL benchmarks for navigation and object manipulation. Videos, source code and pre-trained models are available at the corresponding project website at //facebookresearch.github.io/latent-space-priors .
Differential privacy (DP) provides a robust model to achieve privacy guarantees for released information. We examine the protection potency of sanitized multi-dimensional frequency distributions via DP randomization mechanisms against homogeneity attack (HA). HA allows adversaries to obtain the exact values on sensitive attributes for their targets without having to identify them from the released data. We propose measures for disclosure risk from HA and derive closed-form relationships between the privacy loss parameters in DP and the disclosure risk from HA. The availability of the closed-form relationships assists understanding the abstract concepts of DP and privacy loss parameters by putting them in the context of a concrete privacy attack and offers a perspective for choosing privacy loss parameters when employing DP mechanisms in information sanitization and release in practice. We apply the closed-form mathematical relationships in real-life datasets to demonstrate the assessment of disclosure risk due to HA on differentially private sanitized frequency distributions at various privacy loss parameters.
As data-driven methods are deployed in real-world settings, the processes that generate the observed data will often react to the decisions of the learner. For example, a data source may have some incentive for the algorithm to provide a particular label (e.g. approve a bank loan), and manipulate their features accordingly. Work in strategic classification and decision-dependent distributions seeks to characterize the closed-loop behavior of deploying learning algorithms by explicitly considering the effect of the classifier on the underlying data distribution. More recently, works in performative prediction seek to classify the closed-loop behavior by considering general properties of the mapping from classifier to data distribution, rather than an explicit form. Building on this notion, we analyze repeated risk minimization as the perturbed trajectories of the gradient flows of performative risk minimization. We consider the case where there may be multiple local minimizers of performative risk, motivated by situations where the initial conditions may have significant impact on the long-term behavior of the system. We provide sufficient conditions to characterize the region of attraction for the various equilibria in this settings. Additionally, we introduce the notion of performative alignment, which provides a geometric condition on the convergence of repeated risk minimization to performative risk minimizers.
We introduce weak barycenters of a family of probability distributions, based on the recently developed notion of optimal weak transport of mass by Gozlanet al. (2017) and Backhoff-Veraguas et al. (2020). We provide a theoretical analysis of this object and discuss its interpretation in the light of convex ordering between probability measures. In particular, we show that, rather than averaging the input distributions in a geometric way (as the Wasserstein barycenter based on classic optimal transport does) weak barycenters extract common geometric information shared by all the input distributions, encoded as a latent random variable that underlies all of them. We also provide an iterative algorithm to compute a weak barycenter for a finite family of input distributions, and a stochastic algorithm that computes them for arbitrary populations of laws. The latter approach is particularly well suited for the streaming setting, i.e., when distributions are observed sequentially. The notion of weak barycenter and our approaches to compute it are illustrated on synthetic examples, validated on 2D real-world data and compared to standard Wasserstein barycenters.
Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from using traditional methods to infer potential causal structures from observational data to the field of pattern recognition involved in deep learning. The rapid accumulation of massive data promotes the emergence of causal search methods with brilliant scalability. Existing summaries of causal discovery methods mainly focus on traditional methods based on constraints, scores and FCMs, there is a lack of perfect sorting and elaboration for deep learning-based methods, also lacking some considers and exploration of causal discovery methods from the perspective of variable paradigms. Therefore, we divide the possible causal discovery tasks into three types according to the variable paradigm and give the definitions of the three tasks respectively, define and instantiate the relevant datasets for each task and the final causal model constructed at the same time, then reviews the main existing causal discovery methods for different tasks. Finally, we propose some roadmaps from different perspectives for the current research gaps in the field of causal discovery and point out future research directions.
The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.
The demand for artificial intelligence has grown significantly over the last decade and this growth has been fueled by advances in machine learning techniques and the ability to leverage hardware acceleration. However, in order to increase the quality of predictions and render machine learning solutions feasible for more complex applications, a substantial amount of training data is required. Although small machine learning models can be trained with modest amounts of data, the input for training larger models such as neural networks grows exponentially with the number of parameters. Since the demand for processing training data has outpaced the increase in computation power of computing machinery, there is a need for distributing the machine learning workload across multiple machines, and turning the centralized into a distributed system. These distributed systems present new challenges, first and foremost the efficient parallelization of the training process and the creation of a coherent model. This article provides an extensive overview of the current state-of-the-art in the field by outlining the challenges and opportunities of distributed machine learning over conventional (centralized) machine learning, discussing the techniques used for distributed machine learning, and providing an overview of the systems that are available.
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