Explicit probabilistic models for databases and networks

Recent work in data mining and related areas has highlighted the importance of the statistical assessment of data mining results. Crucial to this endeavour is the choice of a non-trivial null model for the data, to which the found patterns can be contrasted. The most influential null models proposed so far are defined in terms of invariants of the null distribution. Such null models can be used by computation intensive randomization approaches in estimating the statistical significance of data mining results. Here, we introduce a methodology to construct non-trivial probabilistic models based on the maximum entropy (MaxEnt) principle. We show how MaxEnt models allow for the natural incorporation of prior information. Furthermore, they satisfy a number of desirable properties of previously introduced randomization approaches. Lastly, they also have the benefit that they can be represented explicitly. We argue that our approach can be used for a variety of data types. However, for concreteness, we have chosen to demonstrate it in particular for databases and networks.Comment: Submitte

Differential Privacy in Metric Spaces: Numerical, Categorical and Functional Data Under the One Roof

We study Differential Privacy in the abstract setting of Probability on metric spaces. Numerical, categorical and functional data can be handled in a uniform manner in this setting. We demonstrate how mechanisms based on data sanitisation and those that rely on adding noise to query responses fit within this framework. We prove that once the sanitisation is differentially private, then so is the query response for any query. We show how to construct sanitisations for high-dimensional databases using simple 1-dimensional mechanisms. We also provide lower bounds on the expected error for differentially private sanitisations in the general metric space setting. Finally, we consider the question of sufficient sets for differential privacy and show that for relaxed differential privacy, any algebra generating the Borel $\sigma$-algebra is a sufficient set for relaxed differential privacy.Comment: 18 Page

On the Complexity and Approximation of Binary Evidence in Lifted Inference

Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when computing conditional probabilities. The reason is that conditioning on evidence breaks many of the model's symmetries, which can preempt standard lifting techniques. Recent theoretical results show, for example, that conditioning on evidence which corresponds to binary relations is #P-hard, suggesting that no lifting is to be expected in the worst case. In this paper, we balance this negative result by identifying the Boolean rank of the evidence as a key parameter for characterizing the complexity of conditioning in lifted inference. In particular, we show that conditioning on binary evidence with bounded Boolean rank is efficient. This opens up the possibility of approximating evidence by a low-rank Boolean matrix factorization, which we investigate both theoretically and empirically.Comment: To appear in Advances in Neural Information Processing Systems 26 (NIPS), Lake Tahoe, USA, December 201

Detection of Mines in Acoustic Images using Higher Order Spectral Features

A new pattern-recognition algorithm detects approximately 90% of the mines hidden in the Coastal Systems Station Sonar0, 1, and 3 databases of cluttered acoustic images, with about 10% false alarms. Similar to other approaches, the algorithm presented here includes processing the images with an adaptive Wiener filter (the degree of smoothing depends on the signal strength in a local neighborhood) to remove noise without destroying the structural information in the mine shapes, followed by a two-dimensional FIR filter designed to suppress noise and clutter, while enhancing the target signature. A double peak pattern is produced as the FIR filter passes over mine highlight and shadow regions. Although the location, size, and orientation of this pattern within a region of the image can vary, features derived from higher order spectra (HOS) are invariant to translation, rotation, and scaling, while capturing the spatial correlations of mine-like objects. Classification accuracy is improved by combining features based on geometrical properties of the filter output with features based on HOS. The highest accuracy is obtained by fusing classification based on bispectral features with classification based on trispectral features