In this paper we study weighted first-order model counting (WFOMC), which is an important problem (not only) because it can be used for probabilistic inference in most statistical relational learning models [Van den Broeck et al., 2011; Getoor and Taskar, 2007]. Probabilistic inference is in general intractable and the same holds for probabilistic inference in relational domains and therefore also for WFOMC. Lifted inference refers to a set of methods developed in the probabilistic inference literature which exploit structure and symmetries of the problems for making inference more tractable, e.g.

Due to data protection laws sensitive personal data cannot be released or shared among businesses as well as scientific institutions. While anonymization techniques are becoming increasingly popular, they often raise security concerns and have been re-identified in some cases Narayanan and Shmatikov (2010). To be on the safe side, big data collecting organisation such as Eurostat (statistical office of the European Union) or the World Bank only release aggregated summaries of their data. E.g.: Instead of individual salary data only selected quantiles of the population distribution are available. Thus, for exploratory analysis as well as statistical modeling, the need for methods which work on aggregated data is there.

Brad Efron, in his lecture at the occasion of receiving the International Prize in Statistics, brought up some fascinating thoughts on "prediction, estimation and attribution", with particular attention to the new "wide data era" which has entered statistics and data science more generally (Efron, 2019, 2020). Looking back almost 20 years ago, there has been a huge development in statistics since Leo Breiman's article "Statistical Modeling: The Two Cultures" (Breiman, 2001). Even more broadly, data science has become an emerging new field and profession. It deals with information extraction from data, often in close proximity with other sciences. Its historical roots are in statistics, and statistical "critical" thinking plays an ever important role in inference from data to models and prediction. There are many interesting facets of this broad topic, see for example David Donoho's "50 years of Data Science" (Donoho, 2017) or Bin Yu's "Veridical Data Science" (Yu and Kumbier, 2020). Efron (2019, 2020) has formulated intriguing ideas on "prediction, estimation and attribution". We are presenting here a few additional considerations on the topic, as outlined in the following Sections 1.1 and 1.2.

The privacy-preserving federated learning for vertically partitioned data has shown promising results as the solution of the emerging multi-party joint modeling application, in which the data holders (such as government branches, private finance and e-business companies) collaborate throughout the learning process rather than relying on a trusted third party to hold data. However, existing federated learning algorithms for vertically partitioned data are limited to synchronous computation. To improve the efficiency when the unbalanced computation/communication resources are common among the parties in the federated learning system, it is essential to develop asynchronous training algorithms for vertically partitioned data while keeping the data privacy. In this paper, we propose an asynchronous federated SGD (AFSGD-VP) algorithm and its SVRG and SAGA variants on the vertically partitioned data. Moreover, we provide the convergence analyses of AFSGD-VP and its SVRG and SAGA variants under the condition of strong convexity. We also discuss their model privacy, data privacy, computational complexities and communication costs. To the best of our knowledge, AFSGD-VP and its SVRG and SAGA variants are the first asynchronous federated learning algorithms for vertically partitioned data. Extensive experimental results on a variety of vertically partitioned datasets not only verify the theoretical results of AFSGD-VP and its SVRG and SAGA variants, but also show that our algorithms have much higher efficiency than the corresponding synchronous algorithms.

Being able to quickly adapt to changes in dynamics is paramount in model-based control for object manipulation tasks. In order to influence fast adaptation of the inverse dynamics model's parameters, data efficiency is crucial. Given observed data, a key element to how an optimizer updates model parameters is the loss function. In this work, we propose to apply meta-learning to learn structured, state-dependent loss functions during a meta-training phase. We then replace standard losses with our learned losses during online adaptation tasks. We evaluate our proposed approach on inverse dynamics learning tasks, both in simulation and on real hardware data. In both settings, the structured and state-dependent learned losses improve online adaptation speed, when compared to standard, state-independent loss functions.

Objective: Provide guidance on sample size considerations for developing predictive models by empirically establishing the adequate sample size, which balances the competing objectives of improving model performance and reducing model complexity as well as computational requirements. Materials and Methods: We empirically assess the effect of sample size on prediction performance and model complexity by generating learning curves for 81 prediction problems in three large observational health databases, requiring training of 17,248 prediction models. The adequate sample size was defined as the sample size for which the performance of a model equalled the maximum model performance minus a small threshold value. Results: The adequate sample size achieves a median reduction of the number of observations between 9.5% and 78.5% for threshold values between 0.001 and 0.02. The median reduction of the number of predictors in the models at the adequate sample size varied between 8.6% and 68.3%, respectively. Discussion: Based on our results a conservative, yet significant, reduction in sample size and model complexity can be estimated for future prediction work. Though, if a researcher is willing to generate a learning curve a much larger reduction of the model complexity may be possible as suggested by a large outcome-dependent variability. Conclusion: Our results suggest that in most cases only a fraction of the available data was sufficient to produce a model close to the performance of one developed on the full data set, but with a substantially reduced model complexity. 1 Background and significance Physicians infer diagnoses, prognoses, and treatment pathways based on the available medical history of their patients and the current clinical guidelines. Clinical prediction models can support this process by providing risk information on disease presence and progression.[1,2]

In this paper we revisit the problem of private empirical risk minimziation (ERM) with differential privacy. We show that for unconstrained convex empirical risk minimization if the observed gradients of the objective function along the path of private gradient descent lie in a low-dimensional subspace (smaller than the ambient dimensionality of $p$), then using noisy adaptive preconditioning (a.k.a., noisy Adaptive Gradient Descent (AdaGrad)) we obtain a regret composed of two terms: a constant multiplicative factor of the original AdaGrad regret and an additional regret due to noise. In particular, we show that if the gradients lie in a constant rank subspace, then one can achieve an excess empirical risk of $ \tilde{O}(1/\epsilon n)$, compared to the worst-case achievable bound of $\tilde{O}(\sqrt{p}/\epsilon n)$. While previous works show dimension independent excess empirical risk bounds for the restrictive setting of convex generalized linear problems optimized over unconstrained subspaces, our results operate with general convex functions in unconstrained minimization. Along the way, we do a perturbation analysis of noisy AdaGrad, which may be of independent interest.

In many scientific settings there is a need for adaptive experimental design to guide the process of identifying regions of the search space that contain as many true positives as possible subject to a low rate of false discoveries (i.e. false alarms). Such regions of the search space could differ drastically from a predicted set that minimizes 0/1 error and accurate identification could require very different sampling strategies. Like active learning for binary classification, this experimental design cannot be optimally chosen a priori, but rather the data must be taken sequentially and adaptively. However, unlike classification with 0/1 error, collecting data adaptively to find a set with high true positive rate and low false discovery rate (FDR) is not as well understood. In this paper we provide the first provably sample efficient adaptive algorithm for this problem. Along the way we highlight connections between classification, combinatorial bandits, and FDR control making contributions to each.

The projected belief network (PBN) is a layered generative network with tractable likelihood function, and is based on a feed-forward neural network (FF-NN). It can therefore share an embodiment with a discriminative classifier and can inherit the best qualities of both types of network. In this paper, a convolutional PBN is constructed that is both fully discriminative and fully generative and is tested on spectrograms of spoken commands. It is shown that the network displays excellent qualities from either the discriminative or generative viewpoint. Random data synthesis and visible data reconstruction from low-dimensional hidden variables are shown, while classifier performance approaches that of a regularized discriminative network. Combination with a conventional discriminative CNN is also demonstrated.

Identifying optimal values for a high-dimensional set of hyperparameters is a problem that has received growing attention given its importance to large-scale machine learning applications such as neural architecture search. Recently developed optimization methods can be used to select thousands or even millions of hyperparameters. Such methods often yield overfit models, however, leading to poor performance on unseen data. We argue that this overfitting results from using the standard hyperparameter optimization objective function. Here we present an alternative objective that is equivalent to a Probably Approximately Correct-Bayes (PAC-Bayes) bound on the expected out-of-sample error. We then devise an efficient gradient-based algorithm to minimize this objective; the proposed method has asymptotic space and time complexity equal to or better than other gradient-based hyperparameter optimization methods. We show that this new method significantly reduces out-of-sample error when applied to hyperparameter optimization problems known to be prone to overfitting.