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Procedural content generation (PCG) is a growing field, with numerous applications in the video game industry and great potential to help create better games at a fraction of the cost of manual creation. However, much of the work in PCG is focused on generating relatively straightforward levels in simple games, as it is challenging to design an optimisable objective function for complex settings. This limits the applicability of PCG to more complex and modern titles, hindering its adoption in industry. Our work aims to address this limitation by introducing a compositional level generation method that recursively composes simple low-level generators to construct large and complex creations. This approach allows for easily-optimisable objectives and the ability to design a complex structure in an interpretable way by referencing lower-level components. We empirically demonstrate that our method outperforms a non-compositional baseline by more accurately satisfying a designer's functional requirements in several tasks. Finally, we provide a qualitative showcase (in Minecraft) illustrating the large and complex, but still coherent, structures that were generated using simple base generators.

In the literature, the reliability analysis of one-shot devices is found under accelerated life testing in presence of various stress factors. The application of one-shot devices can be extended to the bio-medical field, where often we evidence the emergence of certain diseases under different stress factors due to environmental conditions, lifestyle aspects, presence of co-morbidity etc. In this work, one-shot device data analysis is performed in application to the Murine model for Melioidosis data. The two-parameter logistic exponential distribution is assumed as a lifetime distribution. Weighted minimum density power divergence estimators (WMDPDEs) for robust parameter estimation are obtained along with the conventional maximum likelihood estimators (MLEs). The asymptotic behaviour of the WMDPDEs and testing of the hypothesis based on it are also studied. The performances of estimators are evaluated through extensive simulation experiments. Later those developments are applied to the Murine model for Melioidosis Data. Citing the importance of knowing exactly when to inspect the one-shot devices put to test, a search for optimum inspection times is performed. This optimization is designed to minimize a defined cost function which strikes a trade-off between the precision of the estimation and experimental cost. The search is performed through the population-based heuristic optimization method Genetic Algorithm.

We take a random matrix theory approach to random sketching and show an asymptotic first-order equivalence of the regularized sketched pseudoinverse of a positive semidefinite matrix to a certain evaluation of the resolvent of the same matrix. We focus on real-valued regularization and extend previous results on an asymptotic equivalence of random matrices to the real setting, providing a precise characterization of the equivalence even under negative regularization, including a precise characterization of the smallest nonzero eigenvalue of the sketched matrix, which may be of independent interest. We then further characterize the second-order equivalence of the sketched pseudoinverse. We also apply our results to the analysis of the sketch-and-project method and to sketched ridge regression. Lastly, we prove that these results generalize to asymptotically free sketching matrices, obtaining the resulting equivalence for orthogonal sketching matrices and comparing our results to several common sketches used in practice.

We propose a general purpose confidence interval procedure (CIP) for statistical functionals constructed using data from a stationary time series. The procedures we propose are based on derived distribution-free analogues of the $\chi^2$ and Student's $t$ random variables for the statistical functional context, and hence apply in a wide variety of settings including quantile estimation, gradient estimation, M-estimation, CVAR-estimation, and arrival process rate estimation, apart from more traditional statistical settings. Like the method of subsampling, we use overlapping batches of time series data to estimate the underlying variance parameter; unlike subsampling and the bootstrap, however, we assume that the implied point estimator of the statistical functional obeys a central limit theorem (CLT) to help identify the weak asymptotics (called OB-x limits, x=I,II,III) of batched Studentized statistics. The OB-x limits, certain functionals of the Wiener process parameterized by the size of the batches and the extent of their overlap, form the essential machinery for characterizing dependence, and consequently the correctness of the proposed CIPs. The message from extensive numerical experimentation is that in settings where a functional CLT on the point estimator is in effect, using \emph{large overlapping batches} alongside OB-x critical values yields confidence intervals that are often of significantly higher quality than those obtained from more generic methods like subsampling or the bootstrap. We illustrate using examples from CVaR estimation, ARMA parameter estimation, and NHPP rate estimation; R and MATLAB code for OB-x critical values is available at~\texttt{web.ics.purdue.edu/~pasupath/}.

With the increasing availability of datasets, developing data fusion methods to leverage the strengths of different datasets to draw causal effects is of great practical importance to many scientific fields. In this paper, we consider estimating the quantile treatment effects using small validation data with fully-observed confounders and large auxiliary data with unmeasured confounders. We propose a Fused Quantile Treatment effects Estimator (FQTE) by integrating the information from two datasets based on doubly robust estimating functions. We allow for the misspecification of the models on the dataset with unmeasured confounders. Under mild conditions, we show that the proposed FQTE is asymptotically normal and more efficient than the initial QTE estimator using the validation data solely. By establishing the asymptotic linear forms of related estimators, convenient methods for covariance estimation are provided. Simulation studies demonstrate the empirical validity and improved efficiency of our fused estimators. We illustrate the proposed method with an application.

Algorithms for online learning typically require one or more boundedness assumptions: that the domain is bounded, that the losses are Lipschitz, or both. In this paper, we develop a new setting for online learning with unbounded domains and non-Lipschitz losses. For this setting we provide an algorithm which guarantees $R_{T}(u)\le \tilde O(G\|u\|\sqrt{T}+L\|u\|^{2}\sqrt{T})$ regret on any problem where the subgradients satisfy $\|g_{t}\|\le G+L\|w_{t}\|$, and show that this bound is unimprovable without further assumptions. We leverage this algorithm to develop new saddle-point optimization algorithms that converge in duality gap in unbounded domains, even in the absence of meaningful curvature. Finally, we provide the first algorithm achieving non-trivial dynamic regret in an unbounded domain for non-Lipschitz losses, as well as a matching lower bound. The regret of our dynamic regret algorithm automatically improves to a novel $L^{*}$ bound when the losses are smooth.

Hypothesis transfer learning (HTL) contrasts domain adaptation by allowing for a previous task leverage, named the source, into a new one, the target, without requiring access to the source data. Indeed, HTL relies only on a hypothesis learnt from such source data, relieving the hurdle of expansive data storage and providing great practical benefits. Hence, HTL is highly beneficial for real-world applications relying on big data. The analysis of such a method from a theoretical perspective faces multiple challenges, particularly in classification tasks. This paper deals with this problem by studying the learning theory of HTL through algorithmic stability, an attractive theoretical framework for machine learning algorithms analysis. In particular, we are interested in the statistical behaviour of the regularized empirical risk minimizers in the case of binary classification. Our stability analysis provides learning guarantees under mild assumptions. Consequently, we derive several complexity-free generalization bounds for essential statistical quantities like the training error, the excess risk and cross-validation estimates. These refined bounds allow understanding the benefits of transfer learning and comparing the behaviour of standard losses in different scenarios, leading to valuable insights for practitioners.

The $k$-means algorithm is a prevalent clustering method due to its simplicity, effectiveness, and speed. However, its main disadvantage is its high sensitivity to the initial positions of the cluster centers. The global $k$-means is a deterministic algorithm proposed to tackle the random initialization problem of k-means but its well-known that requires high computational cost. It partitions the data to $K$ clusters by solving all $k$-means sub-problems incrementally for all $k=1,\ldots, K$. For each $k$ cluster problem, the method executes the $k$-means algorithm $N$ times, where $N$ is the number of datapoints. In this paper, we propose the \emph{global $k$-means\texttt{++}} clustering algorithm, which is an effective way of acquiring quality clustering solutions akin to those of global $k$-means with a reduced computational load. This is achieved by exploiting the center selection probability that is effectively used in the $k$-means\texttt{++} algorithm. The proposed method has been tested and compared in various benchmark datasets yielding very satisfactory results in terms of clustering quality and execution speed.

Smart grids are being increasingly deployed worldwide, as they constitute the electricity grid of the future, providing bidirectional communication between households. One of their main potential applications is the peer-to-peer (P2P) energy trading market, which promises users better electricity prices and higher incentives to produce renewable energy. However, most P2P markets require users to submit energy bids/offers in advance, which cannot account for unexpected surpluses of energy consumption/production. Moreover, the fine-grained metering information used in calculating and settling bills/rewards is inherently sensitive and must be protected in conformity with existing privacy regulations. To address these issues, this report proposes a novel privacy-preserving billing and settlements protocol, PPBSP, for use in local energy markets with imperfect bid-offer fulfillment, which only uses homomorphically encrypted versions of the half-hourly user consumption data. PPBSP also supports various cost-sharing mechanisms among market participants, including two new and improved methods of proportionally redistributing the cost of maintaining the balance of the grid in a fair manner. An informal privacy analysis is performed, highlighting the privacy-enhancing characteristics of the protocol, which include metering data and bill confidentiality. PPBSP is also evaluated in terms of computation cost and communication overhead, demonstrating its efficiency and feasibility for markets with varying sizes.

Learning on big data brings success for artificial intelligence (AI), but the annotation and training costs are expensive. In future, learning on small data is one of the ultimate purposes of AI, which requires machines to recognize objectives and scenarios relying on small data as humans. A series of machine learning models is going on this way such as active learning, few-shot learning, deep clustering. However, there are few theoretical guarantees for their generalization performance. Moreover, most of their settings are passive, that is, the label distribution is explicitly controlled by one specified sampling scenario. This survey follows the agnostic active sampling under a PAC (Probably Approximately Correct) framework to analyze the generalization error and label complexity of learning on small data using a supervised and unsupervised fashion. With these theoretical analyses, we categorize the small data learning models from two geometric perspectives: the Euclidean and non-Euclidean (hyperbolic) mean representation, where their optimization solutions are also presented and discussed. Later, some potential learning scenarios that may benefit from small data learning are then summarized, and their potential learning scenarios are also analyzed. Finally, some challenging applications such as computer vision, natural language processing that may benefit from learning on small data are also surveyed.