Positive-unlabeled (PU) learning trains a binary classifier using only positive and unlabeled data. A common simplifying assumption is that the positive data is representative of the target positive class. This assumption is often violated in practice due to time variation, domain shift, or adversarial concept drift. This paper shows that PU learning is possible even with arbitrarily non-representative positive data when provided unlabeled datasets from the source and target distributions. Our key insight is that only the negative class's distribution need be fixed. We propose two methods to learn under such arbitrary positive bias. The first couples negative-unlabeled (NU) learning with unlabeled-unlabeled (UU) learning while the other uses a novel recursive risk estimator robust to positive shift. Experimental results demonstrate our methods' effectiveness across numerous real-world datasets and forms of positive data bias, including disjoint positive class-conditional supports.

Deep learning image classifiers usually rely on huge training sets and their training process can be described as learning the similarities and differences among training images. But, images in large training sets are not usually studied from this perspective and fine-level similarities and differences among images is usually overlooked. Some studies aim to identify the influential and redundant training images, but such methods require a model that is already trained on the entire training set. Here, we show that analyzing the contents of large training sets can provide valuable insights about the classification task at hand, prior to training a model on them. We use wavelet decomposition of images and other image processing tools to perform such analysis, with no need for a pre-trained model. This makes the analysis of training sets, straightforward and fast. We show that similar images in standard datasets (such as CIFAR) can be identified in a few seconds, a significant speed-up compared to alternative methods in the literature. We also show that similarities between training and testing images may explain the generalization of models and their mistakes. Finally, we investigate the similarities between images in relation to decision boundaries of a trained model.

The Dirichlet Belief Network~(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. In this work, we leverage its interpretable modelling architecture and propose a deep dynamic probabilistic framework -- the Recurrent Dirichlet Belief Network~(Recurrent-DBN) -- to study interpretable hidden structures from dynamic relational data. The proposed Recurrent-DBN has the following merits: (1) it infers interpretable and organised hierarchical latent structures for objects within and across time steps; (2) it enables recurrent long-term temporal dependence modelling, which outperforms the one-order Markov descriptions in most of the dynamic probabilistic frameworks. In addition, we develop a new inference strategy, which first upward-and-backward propagates latent counts and then downward-and-forward samples variables, to enable efficient Gibbs sampling for the Recurrent-DBN. We apply the Recurrent-DBN to dynamic relational data problems. The extensive experiment results on real-world data validate the advantages of the Recurrent-DBN over the state-of-the-art models in interpretable latent structure discovery and improved link prediction performance.

We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regularization schemes in Hilbert scale. We discuss the rates of convergence for the regularized solution under the prior assumptions and a certain link condition. We express the error in terms of certain distance functions. For regression functions with smoothness given in terms of source conditions the error bound can then be explicitly established.

Classifier calibration does not always go hand in hand with the classifier's ability to separate the classes. There are applications where good classifier calibration, i.e. the ability to produce accurate probability estimates, is more important than class separation. When the amount of data for training is limited, the traditional approach to improve calibration starts to crumble. In this article we show how generating more data for calibration is able to improve calibration algorithm performance in many cases where a classifier is not naturally producing well-calibrated outputs and the traditional approach fails. The proposed approach adds computational cost but considering that the main use case is with small data sets this extra computational cost stays insignificant and is comparable to other methods in prediction time. From the tested classifiers the largest improvement was detected with the random forest and naive Bayes classifiers. Therefore, the proposed approach can be recommended at least for those classifiers when the amount of data available for training is limited and good calibration is essential.

We present a novel learning framework that consistently embeds underlying physics while bypassing a significant drawback of most modern, data-driven coarse-grained approaches in the context of molecular dynamics (MD), i.e., the availability of big data. The generation of a sufficiently large training dataset poses a computationally demanding task, while complete coverage of the atomistic configuration space is not guaranteed. As a result, the explorative capabilities of data-driven coarse-grained models are limited and may yield biased "predictive" tools. We propose a novel objective based on reverse Kullback-Leibler divergence that fully incorporates the available physics in the form of the atomistic force field. Rather than separating model learning from the data-generation procedure - the latter relies on simulating atomistic motions governed by force fields - we query the atomistic force field at sample configurations proposed by the predictive coarse-grained model. Thus, learning relies on the evaluation of the force field but does not require any MD simulation. The resulting generative coarse-grained model serves as an efficient surrogate model for predicting atomistic configurations and estimating relevant observables. Beyond obtaining a predictive coarse-grained model, we demonstrate that in the discovered lower-dimensional representation, the collective variables (CVs) are related to physicochemical properties, which are essential for gaining understanding of unexplored complex systems. We demonstrate the algorithmic advances in terms of predictive ability and the physical meaning of the revealed CVs for a bimodal potential energy function and the alanine dipeptide.

Real-world data often presents itself in the form of a network. Examples include social networks, citation networks, biological networks, and knowledge graphs. In their simplest form, networks represent real-life entities (e.g. people, papers, proteins, concepts) as nodes, and describe them in terms of their relations with other entities by means of edges between these nodes. This can be valuable for a range of purposes from the study of information diffusion to bibliographic analysis, bioinformatics research, and question-answering. The quality of networks is often problematic though, affecting downstream tasks. This paper focuses on the common problem where a node in the network in fact corresponds to multiple real-life entities. In particular, we introduce FONDUE, an algorithm based on network embedding for node disambiguation. Given a network, FONDUE identifies nodes that correspond to multiple entities, for subsequent splitting. Extensive experiments on twelve benchmark datasets demonstrate that FONDUE is substantially and uniformly more accurate for ambiguous node identification compared to the existing state-of-the-art, at a comparable computational cost, while less optimal for determining the best way to split ambiguous nodes.

We characterize Bayesian regret in a stochastic multi-armed bandit problem with a large but finite number of arms. In particular, we assume the number of arms $k$ is $T^{\alpha}$, where $T$ is the time-horizon and $\alpha$ is in $(0,1)$. We consider a Bayesian setting where the reward distribution of each arm is drawn independently from a common prior, and provide a complete analysis of expected regret with respect to this prior. Our results exhibit a sharp distinction around $\alpha = 1/2$. When $\alpha < 1/2$, the fundamental lower bound on regret is $\Omega(k)$; and it is achieved by a standard UCB algorithm. When $\alpha > 1/2$, the fundamental lower bound on regret is $\Omega(\sqrt{T})$, and it is achieved by an algorithm that first subsamples $\sqrt{T}$ arms uniformly at random, then runs UCB on just this subset. Interestingly, we also find that a sufficiently large number of arms allows the decision-maker to benefit from "free" exploration if she simply uses a greedy algorithm. In particular, this greedy algorithm exhibits a regret of $\tilde{O}(\max(k,T/\sqrt{k}))$, which translates to a {\em sublinear} (though not optimal) regret in the time horizon. We show empirically that this is because the greedy algorithm rapidly disposes of underperforming arms, a beneficial trait in the many-armed regime. Technically, our analysis of the greedy algorithm involves a novel application of the Lundberg inequality, an upper bound for the ruin probability of a random walk; this approach may be of independent interest.

The point estimates of ReLU classification networks---arguably the most widely used neural network architecture---have been shown to yield arbitrarily high confidence far away from the training data. This architecture, in conjunction with a maximum a posteriori estimation scheme, is thus not calibrated nor robust. Approximate Bayesian inference has been empirically demonstrated to improve predictive uncertainty in neural networks, although the theoretical analysis of such Bayesian approximations is limited. We theoretically analyze approximate Gaussian posterior distributions on the weights of ReLU networks and show that they fix the overconfidence problem. Furthermore, we show that even a simplistic, thus cheap, Bayesian approximation, also fixes these issues. This indicates that a sufficient condition for a calibrated uncertainty on a ReLU network is ``to be a bit Bayesian''. These theoretical results validate the usage of last-layer Bayesian approximation and motivate a range of a fidelity-cost trade-off. We further validate these findings empirically via various standard experiments using common deep ReLU networks and Laplace approximations.

We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean field games (MFGs). Our algorithm is geared toward high-dimensional instances MFGs that are beyond reach with existing solution methods. We achieve this in two steps. First, we take advantage of the underlying variational primal-dual structure that MFGs exhibit and phrase it as a convex-concave saddle point problem. Second, we parameterize the value and density functions by two neural networks, respectively. By phrasing the problem in this manner, solving the MFG can be interpreted as a special case of training a generative adversarial generative network (GAN). We show the potential of our method on up to 50-dimensional MFG problems.