The display advertising industry has recently transitioned from second- to first-price auctions as its primary mechanism for ad allocation and pricing. In light of this, publishers need to re-evaluate and optimize their auction parameters, notably reserve prices. In this paper, we propose a gradient-based algorithm to adaptively update and optimize reserve prices based on estimates of bidders' responsiveness to experimental shocks in reserves. Our key innovation is to draw on the inherent structure of the revenue objective in order to reduce the variance of gradient estimates and improve convergence rates in both theory and practice. We show that revenue in a first-price auction can be usefully decomposed into a \emph{demand} component and a \emph{bidding} component, and introduce techniques to reduce the variance of each component. We characterize the bias-variance trade-offs of these techniques and validate the performance of our proposed algorithm through experiments on synthetic data and real display ad auctions data from Google ad exchange.

Data collected at very frequent intervals is usually extremely sparse and has no structure that is exploitable by modern tensor decomposition algorithms. Thus the utility of such tensors is low, in terms of the amount of interpretable and exploitable structure that one can extract from them. In this paper, we introduce the problem of finding a tensor of adaptive aggregated granularity that can be decomposed to reveal meaningful latent concepts (structures) from datasets that, in their original form, are not amenable to tensor analysis. Such datasets fall under the broad category of sparse point processes that evolve over space and/or time. To the best of our knowledge, this is the first work that explores adaptive granularity aggregation in tensors. Furthermore, we formally define the problem and discuss what different definitions of "good structure" can be in practice, and show that optimal solution is of prohibitive combinatorial complexity. Subsequently, we propose an efficient and effective greedy algorithm which follows a number of intuitive decision criteria that locally maximize the "goodness of structure", resulting in high-quality tensors. We evaluate our method on both semi-synthetic data where ground truth is known and real datasets for which we do not have any ground truth. In both cases, our proposed method constructs tensors that have very high structure quality. Finally, our proposed method is able to discover different natural resolutions of a multi-aspect dataset, which can lead to multi-resolution analysis.

Non-negativematrix factorization (NMF) is a dimensionality reduction technique whichtends to produce a sparse representation of data. Commonly, the error between the actual and recreated matrices is used as an objective function, butthis method may not produce the type of representation we desire as it allows for the complexity of the model to grow, constrained only by the size of the subspace and the non-negativity requirement. If additional constraints, such as sparsity, are imposed the question of parameter selection becomes critical. Insteadof adding sparsity constraints in an ad-hoc manner we propose a novel objective function created by using the principle of minimum description length (MDL). Our formulation, MDL-NMF, automatically trades off between the complexity and accuracy of the model using a principled approach with little parameter selection or the need for domain expertise. We demonstrate our model works effectively on three heterogeneous data-sets and on a range of semisynthetic data showing the broad applicability of our method. Keywords: nonnegative matrix factorisation, minimum description length, model selection 1. Introduction Nonnegative matrix factorisation (NMF) is a popular linear dimensionality reduction technique. Its ability to produce a sparse and parts based representation, incontrast to principal component analysis (PCA) which is variance preserving, has been exploited in a range of applications [1, 2, 3].

We explore the problem of learning under selective labels in the context of algorithm-assisted decision making. Selective labels is a pervasive selection bias problem that arises when historical decision making blinds us to the true outcome for certain instances. Examples of this are common in many applications, ranging from predicting recidivism using pre-trial release data to diagnosing patients. In this paper we discuss why selective labels often cannot be effectively tackled by standard methods for adjusting for sample selection bias, even if there are no unobservables. We propose a data augmentation approach that can be used to either leverage expert consistency to mitigate the partial blindness that results from selective labels, or to empirically validate whether learning under such framework may lead to unreliable models prone to systemic discrimination.