Unsupervised Learning under Latent Label Shift

What sorts of structure might enable a learner to discover classes from unlabeled data? Traditional approaches rely on feature-space similarity and heroic assumptions on the data. In this paper, we introduce unsupervised learning under Latent Label Shift (LLS), where we have access to unlabeled data from multiple domains such that the label marginals $p_d(y)$ can shift across domains but the class conditionals $p(\mathbf{x}|y)$ do not. This work instantiates a new principle for identifying classes: elements that shift together group together. For finite input spaces, we establish an isomorphism between LLS and topic modeling: inputs correspond to words, domains to documents, and labels to topics. Addressing continuous data, we prove that when each label's support contains a separable region, analogous to an anchor word, oracle access to $p(d|\mathbf{x})$ suffices to identify $p_d(y)$ and $p_d(y|\mathbf{x})$ up to permutation. Thus motivated, we introduce a practical algorithm that leverages domain-discriminative models as follows: (i) push examples through domain discriminator $p(d|\mathbf{x})$; (ii) discretize the data by clustering examples in $p(d|\mathbf{x})$ space; (iii) perform non-negative matrix factorization on the discrete data; (iv) combine the recovered $p(y|d)$ with the discriminator outputs $p(d|\mathbf{x})$ to compute $p_d(y|x) \; \forall d$. With semi-synthetic experiments, we show that our algorithm can leverage domain information to improve state of the art unsupervised classification methods. We reveal a failure mode of standard unsupervised classification methods when feature-space similarity does not indicate true groupings, and show empirically that our method better handles this case. Our results establish a deep connection between distribution shift and topic modeling, opening promising lines for future work.

Ant Colony Inspired Machine Learning Algorithm for Identifying and Emulating Virtual Sensors

The scale of systems employed in industrial environments demands a large number of sensors to facilitate meticulous monitoring and functioning. These requirements could potentially lead to inefficient system designs. The data coming from various sensors are often correlated due to the underlying relations in the system parameters that the sensors monitor. In theory, it should be possible to emulate the output of certain sensors based on other sensors. Tapping into such possibilities holds tremendous advantages in terms of reducing system design complexity. In order to identify the subset of sensors whose readings can be emulated, the sensors must be grouped into clusters. Complex systems generally have a large quantity of sensors that collect and store data over prolonged periods of time. This leads to the accumulation of massive amounts of data. In this paper we propose an end-to-end algorithmic solution, to realise virtual sensors in such systems. This algorithm splits the dataset into blocks and clusters each of them individually. It then fuses these clustering solutions to obtain a global solution using an Ant Colony inspired technique, FAC2T. Having grouped the sensors into clusters, we select representative sensors from each cluster. These sensors are retained in the system while the other sensors readings are emulated by applying supervised learning algorithms.