We have utilized the non-conjugate VB method for the problem of the sparse Poisson regression model. To provide an approximated conjugacy in the model, the likelihood is approximated by a quadratic function, which provides the conjugacy of the approximation component with the Gaussian prior to the regression coefficient. Three sparsity-enforcing priors are used for this problem. The proposed models are compared with each other and two frequentist sparse Poisson methods (LASSO and SCAD) to evaluate the prediction performance, as well as, the sparsing performance of the proposed methods. Throughout a simulated data example, the accuracy of the VB methods is computed compared to the corresponding benchmark MCMC methods. It can be observed that the proposed VB methods have provided a good approximation to the posterior distribution of the parameters, while the VB methods are much faster than the MCMC ones. Using several benchmark count response data sets, the prediction performance of the proposed methods is evaluated in real-world applications.
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Capturing the underlying structural causal relations represented by Directed Acyclic Graphs (DAGs) has been a fundamental task in various AI disciplines. Causal DAG learning via the continuous optimization framework has recently achieved promising performance in terms of both accuracy and efficiency. However, most methods make strong assumptions of homoscedastic noise, i.e., exogenous noises have equal variances across variables, observations, or even both. The noises in real data usually violate both assumptions due to the biases introduced by different data collection processes. To address the issue of heteroscedastic noise, we introduce relaxed and implementable sufficient conditions, proving the identifiability of a general class of SEM subject to these conditions. Based on the identifiable general SEM, we propose a novel formulation for DAG learning that accounts for the variation in noise variance across variables and observations. We then propose an effective two-phase iterative DAG learning algorithm to address the increasing optimization difficulties and to learn a causal DAG from data with heteroscedastic variable noise under varying variance. We show significant empirical gains of the proposed approaches over state-of-the-art methods on both synthetic data and real data.
Model counting, or counting the satisfying assignments of a Boolean formula, is a fundamental problem with diverse applications. Given #P-hardness of the problem, developing algorithms for approximate counting is an important research area. Building on the practical success of SAT-solvers, the focus has recently shifted from theory to practical implementations of approximate counting algorithms. This has brought to focus new challenges, such as the design of auditable approximate counters that not only provide an approximation of the model count, but also a certificate that a verifier with limited computational power can use to check if the count is indeed within the promised bounds of approximation. Towards generating certificates, we start by examining the best-known deterministic approximate counting algorithm that uses polynomially many calls to a $\Sigma_2^P$ oracle. We show that this can be audited via a $\Sigma_2^P$ oracle with the query constructed over $n^2 \log^2 n$ variables, where the original formula has $n$ variables. Since $n$ is often large, we ask if the count of variables in the certificate can be reduced -- a crucial question for potential implementation. We show that this is indeed possible with a tradeoff in the counting algorithm's complexity. Specifically, we develop new deterministic approximate counting algorithms that invoke a $\Sigma_3^P$ oracle, but can be certified using a $\Sigma_2^P$ oracle using certificates on far fewer variables: our final algorithm uses only $n \log n$ variables. Our study demonstrates that one can simplify auditing significantly if we allow the counting algorithm to access a slightly more powerful oracle. This shows for the first time how audit complexity can be traded for complexity of approximate counting.
We consider the problem of policy transfer between two Markov Decision Processes (MDPs). We introduce a lemma based on existing theoretical results in reinforcement learning to measure the relativity gap between two arbitrary MDPs, that is the difference between any two cumulative expected returns defined on different policies and environment dynamics. Based on this lemma, we propose two new algorithms referred to as Relative Policy Optimization (RPO) and Relative Transition Optimization (RTO), which offer fast policy transfer and dynamics modelling, respectively. RPO transfers the policy evaluated in one environment to maximize the return in another, while RTO updates the parameterized dynamics model to reduce the gap between the dynamics of the two environments. Integrating the two algorithms results in the complete Relative Policy-Transition Optimization (RPTO) algorithm, in which the policy interacts with the two environments simultaneously, such that data collections from two environments, policy and transition updates are completed in one closed loop to form a principled learning framework for policy transfer. We demonstrate the effectiveness of RPTO on a set of MuJoCo continuous control tasks by creating policy transfer problems via variant dynamics.
Word problem Solving is a challenging NLP task that deals with solving mathematical problems described in natural language. Recently, there has been renewed interest in developing word problem solvers for Indian languages. As part of this paper, we have built a Hindi arithmetic word problem solver which makes use of verbs. Additionally, we have created verb categorization data for Hindi. Verbs are very important for solving word problems with addition/subtraction operations as they help us identify the set of operations required to solve the word problems. We propose a rule-based solver that uses verb categorisation to identify operations in a word problem and generate answers for it. To perform verb categorisation, we explore several approaches and present a comparative study.
Diversity optimization seeks to discover a set of solutions that elicit diverse features. Prior work has proposed Novelty Search (NS), which, given a current set of solutions, seeks to expand the set by finding points in areas of low density in the feature space. However, to estimate density, NS relies on a heuristic that considers the k-nearest neighbors of the search point in the feature space, which yields a weaker stability guarantee. We propose Density Descent Search (DDS), an algorithm that explores the feature space via gradient descent on a continuous density estimate of the feature space that also provides stronger stability guarantee. We experiment with DDS and two density estimation methods: kernel density estimation (KDE) and continuous normalizing flow (CNF). On several standard diversity optimization benchmarks, DDS outperforms NS, the recently proposed MAP-Annealing algorithm, and other state-of-the-art baselines. Additionally, we prove that DDS with KDE provides stronger stability guarantees than NS, making it more suitable for adaptive optimizers. Furthermore, we prove that NS is a special case of DDS that descends a KDE of the feature space.
Data in Knowledge Graphs often represents part of the current state of the real world. Thus, to stay up-to-date the graph data needs to be updated frequently. To utilize information from Knowledge Graphs, many state-of-the-art machine learning approaches use embedding techniques. These techniques typically compute an embedding, i.e., vector representations of the nodes as input for the main machine learning algorithm. If a graph update occurs later on -- specifically when nodes are added or removed -- the training has to be done all over again. This is undesirable, because of the time it takes and also because downstream models which were trained with these embeddings have to be retrained if they change significantly. In this paper, we investigate embedding updates that do not require full retraining and evaluate them in combination with various embedding models on real dynamic Knowledge Graphs covering multiple use cases. We study approaches that place newly appearing nodes optimally according to local information, but notice that this does not work well. However, we find that if we continue the training of the old embedding, interleaved with epochs during which we only optimize for the added and removed parts, we obtain good results in terms of typical metrics used in link prediction. This performance is obtained much faster than with a complete retraining and hence makes it possible to maintain embeddings for dynamic Knowledge Graphs.
Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different learning objectives. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results on these tasks, and consistently outperforms baselines on these tasks.
We study the problem of textual relation embedding with distant supervision. To combat the wrong labeling problem of distant supervision, we propose to embed textual relations with global statistics of relations, i.e., the co-occurrence statistics of textual and knowledge base relations collected from the entire corpus. This approach turns out to be more robust to the training noise introduced by distant supervision. On a popular relation extraction dataset, we show that the learned textual relation embedding can be used to augment existing relation extraction models and significantly improve their performance. Most remarkably, for the top 1,000 relational facts discovered by the best existing model, the precision can be improved from 83.9% to 89.3%.
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