Dhruti Shah

Matthias Minder, Zahra Farsijani, Dhruti Shah et al.

In many applications, a dataset can be considered as a set of observed signals that live on an unknown underlying graph structure. Some of these signals may be seen as white noise that has been filtered on the graph topology by a graph filter. Hence, the knowledge of the filter and the graph provides valuable information about the underlying data generation process and the complex interactions that arise in the dataset. We hence introduce a novel graph signal processing framework for jointly learning the graph and its generating filter from signal observations. We cast a new optimisation problem that minimises the Wasserstein distance between the distribution of the signal observations and the filtered signal distribution model. Our proposed method outperforms state-of-the-art graph learning frameworks on synthetic data. We then apply our method to a temperature anomaly dataset, and further show how this framework can be used to infer missing values if only very little information is available.

Dhruti Shah, Tuhinangshu Choudhury, Nikhil Karamchandani et al.

We consider the problem of adaptively PAC-learning a probability distribution $\mathcal{P}$'s mode by querying an oracle for information about a sequence of i.i.d. samples $X_1, X_2, \ldots$ generated from $\mathcal{P}$. We consider two different query models: (a) each query is an index $i$ for which the oracle reveals the value of the sample $X_i$, (b) each query is comprised of two indices $i$ and $j$ for which the oracle reveals if the samples $X_i$ and $X_j$ are the same or not. For these query models, we give sequential mode-estimation algorithms which, at each time $t$, either make a query to the corresponding oracle based on past observations, or decide to stop and output an estimate for the distribution's mode, required to be correct with a specified confidence. We analyze the query complexity of these algorithms for any underlying distribution $\mathcal{P}$, and derive corresponding lower bounds on the optimal query complexity under the two querying models.