**Generalized Separable Nonnegative Matrix Factorization (GS-NMF)**

Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and hyperspectral unmixing. Given a data matrix $M$ and a factorization rank $r$, NMF looks for a nonnegative matrix $W$ with $r$ columns and a nonnegative matrix $H$ with $r$ rows such that $M \approx WH$. NMF is NP-hard to solve in general. However, it can be computed efficiently under the separability assumption which requires that the basis vectors appear as data points, that is, that there exists an index set $\mathcal{K}$ such that $W = M(:,\mathcal{K})$. In this paper, we generalize the separability assumption: We only require that for each rank-one factor $W(:,k)H(k,:)$ for $k=1,2,\dots,r$, either $W(:,k) = M(:,j)$ for some $j$ or $H(k,:) = M(i,:)$ for some $i$. We refer to the corresponding problem as generalized separable NMF (GS-NMF). We discuss some properties of GS-NMF and propose a convex optimization model which we solve using a fast gradient method. We also propose a heuristic algorithm inspired by the successive projection algorithm. To verify the effectiveness of our methods, we compare them with several state-of-the-art separable NMF algorithms on synthetic, document and image data sets. … **Reconciliation k-Median**

We propose a new variant of the k-median problem, where the objective function models not only the cost of assigning data points to cluster representatives, but also a penalty term for disagreement among the representatives. We motivate this novel problem by applications where we are interested in clustering data while avoiding selecting representatives that are too far from each other. For example, we may want to summarize a set of news sources, but avoid selecting ideologically-extreme articles in order to reduce polarization. To solve the proposed k-median formulation we adopt the local-search algorithm of Arya et al. We show that the algorithm provides a provable approximation guarantee, which becomes constant under a mild assumption on the minimum number of points for each cluster. We experimentally evaluate our problem formulation and proposed algorithm on datasets inspired by the motivating applications. In particular, we experiment with data extracted from Twitter, the US Congress voting records, and popular news sources. The results show that our objective can lead to choosing less polarized groups of representatives without significant loss in representation fidelity. … **Fast Context Adaptation via Meta-Learning (CAML)**

We propose CAML, a meta-learning method for fast adaptation that partitions the model parameters into two parts: context parameters that serve as additional input to the model and are adapted on individual tasks, and shared parameters that are meta-trained and shared across tasks. At test time, the context parameters are updated with one or several gradient steps on a task-specific loss that is backpropagated through the shared part of the network. Compared to approaches that adjust all parameters on a new task (e.g., MAML), our method can be scaled up to larger networks without overfitting on a single task, is easier to implement, and saves memory writes during training and network communication at test time for distributed machine learning systems. We show empirically that this approach outperforms MAML, is less sensitive to the task-specific learning rate, can capture meaningful task embeddings with the context parameters, and outperforms alternative partitionings of the parameter vectors. … **Transferable Dialogue State Generator (TRADE)**

In this thesis, we leverage the neural copy mechanism and memory-augmented neural networks (MANNs) to address existing challenge of neural task-oriented dialogue learning. We show the effectiveness of our strategy by achieving good performance in multi-domain dialogue state tracking, retrieval-based dialogue systems, and generation-based dialogue systems. We first propose a transferable dialogue state generator (TRADE) that leverages its copy mechanism to get rid of dialogue ontology and share knowledge between domains. We also evaluate unseen domain dialogue state tracking and show that TRADE enables zero-shot dialogue state tracking and can adapt to new few-shot domains without forgetting the previous domains. Second, we utilize MANNs to improve retrieval-based dialogue learning. They are able to capture dialogue sequential dependencies and memorize long-term information. We also propose a recorded delexicalization copy strategy to replace real entity values with ordered entity types. Our models are shown to surpass other retrieval baselines, especially when the conversation has a large number of turns. Lastly, we tackle generation-based dialogue learning with two proposed models, the memory-to-sequence (Mem2Seq) and global-to-local memory pointer network (GLMP). Mem2Seq is the first model to combine multi-hop memory attention with the idea of the copy mechanism. GLMP further introduces the concept of response sketching and double pointers copying. We show that GLMP achieves the state-of-the-art performance on human evaluation. …

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