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Union-free codes and disjunctive codes are two combinatorial structures, which are used in nonadaptive group testing to find a set of $d$ defective elements among $n$ samples by carrying out the minimal number of tests $t$. It is known that union-free codes have a larger rate, whereas disjunctive codes provide a more efficient decoding algorithm. In this paper we introduce a new family of codes for nonadaptive group testing with fast decoding. The rate of these codes is larger than the rate of disjunctive codes, while the decoding algorithm has the same complexity. In addition, we derive a lower bound on the rate of new codes for the case of $d=2$ defectives, which is significantly better than the bound for disjunctive codes and almost as good as the bound for union-free codes.

In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate that these algorithms not only enjoy a linear rate of convergence in the absence of convexity, but also attain the optimal statistical rate (i.e., minimax rate). By introducing the generic chaining, our analysis removes the impractical resampling assumption used in the previous work. Moreover, our results also reveal a time-data tradeoff in this covariate adjusted precision matrix estimation problem. Numerical experiments are provided to verify our theoretical results.

Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult. Here we investigate the properties of certain algebraic hypersurfaces over finite fields, whose intersection numbers with any hyperplane only takes a few values; these varieties give rise to $q$-divisible linear codes with at most $5$ weights. Furthermore, for $q$ odd these codes turn out to be minimal and we characterize the access structures of the secret sharing schemes based on their dual codes. Indeed, the secret sharing schemes thus obtained are democratic, that is each participant belongs to the same number of minimal access sets and can easily be described.

ConsumerCheck is an open source data analysis software tailored for analysis of sensory and consumer data. Since some of the implemented methods are generic, such as PCA, PLSR and PCR, other data from other domains may also be analysed with ConsumerCheck. The software comes with a graphical user interface and as such provides non-statisticians and users without programming skills free access to a number of widely used analysis methods within the field of sensory and consumer science. Computational results are presented in plots that are easily generated from the tree-controls within the graphical user interfaces. Since the construction of conjoint analysis models is not always straightforward, ConsumerCheck provides three previously defined model structures of different complexity. ConsumerCheck is an ongoing research project and the objective is to implement further statistical methods over time.

We develop a method to study sufficient conditions for perfect mixed tilings. Our framework allows the embedding of bounded degree graphs $H$ with components of sublinear order. As a corollary, we recover and extend the work of K\"uhn and Osthus regarding sufficient minimum degree conditions for perfect $F$-tilings (for an arbitrary fixed graph $F$) by replacing the $F$-tiling with the aforementioned graphs $H$. Moreover, we obtain analogous results for degree sequences and in the setting of uniformly dense graphs. Finally, we asymptotically resolve a conjecture of Koml\'os in a strong sense.

Reward is the driving force for reinforcement-learning agents. This paper is dedicated to understanding the expressivity of reward as a way to capture tasks that we would want an agent to perform. We frame this study around three new abstract notions of "task" that might be desirable: (1) a set of acceptable behaviors, (2) a partial ordering over behaviors, or (3) a partial ordering over trajectories. Our main results prove that while reward can express many of these tasks, there exist instances of each task type that no Markov reward function can capture. We then provide a set of polynomial-time algorithms that construct a Markov reward function that allows an agent to optimize tasks of each of these three types, and correctly determine when no such reward function exists. We conclude with an empirical study that corroborates and illustrates our theoretical findings.

The collective attention on online items such as web pages, search terms, and videos reflects trends that are of social, cultural, and economic interest. Moreover, attention trends of different items exhibit mutual influence via mechanisms such as hyperlinks or recommendations. Many visualisation tools exist for time series, network evolution, or network influence; however, few systems connect all three. In this work, we present AttentionFlow, a new system to visualise networks of time series and the dynamic influence they have on one another. Centred around an ego node, our system simultaneously presents the time series on each node using two visual encodings: a tree ring for an overview and a line chart for details. AttentionFlow supports interactions such as overlaying time series of influence and filtering neighbours by time or flux. We demonstrate AttentionFlow using two real-world datasets, VevoMusic and WikiTraffic. We show that attention spikes in songs can be explained by external events such as major awards, or changes in the network such as the release of a new song. Separate case studies also demonstrate how an artist's influence changes over their career, and that correlated Wikipedia traffic is driven by cultural interests. More broadly, AttentionFlow can be generalised to visualise networks of time series on physical infrastructures such as road networks, or natural phenomena such as weather and geological measurements.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space, such as the simplex, the time-discretisation error can dominate when we are near the boundary of the space. We demonstrate that while current SGMCMC methods for the simplex perform well in certain cases, they struggle with sparse simplex spaces; when many of the components are close to zero. However, most popular large-scale applications of Bayesian inference on simplex spaces, such as network or topic models, are sparse. We argue that this poor performance is due to the biases of SGMCMC caused by the discretization error. To get around this, we propose the stochastic CIR process, which removes all discretization error and we prove that samples from the stochastic CIR process are asymptotically unbiased. Use of the stochastic CIR process within a SGMCMC algorithm is shown to give substantially better performance for a topic model and a Dirichlet process mixture model than existing SGMCMC approaches.

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.