Knowledge graph reasoning is the fundamental component to support machine learning applications such as information extraction, information retrieval and recommendation. Since knowledge graph can be viewed as the discrete symbolic representations of knowledge, reasoning on knowledge graphs can naturally leverage the symbolic techniques. However, symbolic reasoning is intolerant of the ambiguous and noisy data. On the contrary, the recent advances of deep learning promote neural reasoning on knowledge graphs, which is robust to the ambiguous and noisy data, but lacks interpretability compared to symbolic reasoning. Considering the advantages and disadvantages of both methodologies, recent efforts have been made on combining the two reasoning methods. In this survey, we take a thorough look at the development of the symbolic reasoning, neural reasoning and the neural-symbolic reasoning on knowledge graphs. We survey two specific reasoning tasks, knowledge graph completion and question answering on knowledge graphs, and explain them in a unified reasoning framework. We also briefly discuss the future directions for knowledge graph reasoning.

We present a theoretical and algorithmic study of the multiple-source domain adaptation problem in the common scenario where the learner has access only to a limited amount of labeled target data, but where the learner has at disposal a large amount of labeled data from multiple source domains. We show that a new family of algorithms based on model selection ideas benefits from very favorable guarantees in this scenario and discuss some theoretical obstacles affecting some alternative techniques. We also report the results of several experiments with our algorithms that demonstrate their practical effectiveness.

We develop a new approach to obtaining high probability regret bounds for online learning with bandit feedback against an adaptive adversary. While existing approaches all require carefully constructing optimistic and biased loss estimators, our approach uses standard unbiased estimators and relies on a simple increasing learning rate schedule, together with the help of logarithmically homogeneous self-concordant barriers and a strengthened Freedman's inequality. Besides its simplicity, our approach enjoys several advantages. First, the obtained high-probability regret bounds are data-dependent and could be much smaller than the worst-case bounds, which resolves an open problem asked by Neu (2015). Second, resolving another open problem of Bartlett et al. (2008) and Abernethy and Rakhlin (2009), our approach leads to the first general and efficient algorithm with a high-probability regret bound for adversarial linear bandits, while previous methods are either inefficient or only applicable to specific action sets. Finally, our approach can also be applied to learning adversarial Markov Decision Processes and provides the first algorithm with a high-probability small-loss bound for this problem.

We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a regular (aperiodic and irreducible) finite Markov chain. Specially, consider a random walk on a regular Markov chain and a Hermitian matrix-valued function on its state space. Our result gives exponentially decreasing bounds on the tail distributions of the extreme eigenvalues of the sample mean matrix. Our proof is based on the matrix expander (regular undirected graph) Chernoff bound [Garg et al. STOC '18] and scalar Chernoff-Hoeffding bounds for Markov chains [Chung et al. STACS '12]. Our matrix Chernoff bound for Markov chains can be applied to analyze the behavior of co-occurrence statistics for sequential data, which have been common and important data signals in machine learning. We show that given a regular Markov chain with $n$ states and mixing time $\tau$, we need a trajectory of length $O(\tau (\log{(n)}+\log{(\tau)})/\epsilon^2)$ to achieve an estimator of the co-occurrence matrix with error bound $\epsilon$. We conduct several experiments and the experimental results are consistent with the exponentially fast convergence rate from theoretical analysis. Our result gives the first bound on the convergence rate of the co-occurrence matrix and the first sample complexity analysis in graph representation learning.

Non-Intrusive Load Monitoring (NILM) aims to predict the status or consumption of domestic appliances in a household only by knowing the aggregated power load. NILM can be formulated as regression problem or most often as a classification problem. Most datasets gathered by smart meters allow to define naturally a regression problem, but the corresponding classification problem is a derived one, since it requires a conversion from the power signal to the status of each device by a thresholding method. We treat three different thresholding methods to perform this task, discussing their differences on various devices from the UK-DALE dataset. We analyze the performance of deep learning state-of-the-art architectures on both the regression and classification problems, introducing criteria to select the most convenient thresholding method.

We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample complexity scaling logarithmically with the number of variables, as in the discrete and Gaussian settings. Our approach is applicable to a large class of pairwise MRFs with continuous variables and also has desirable asymptotic properties, including consistency and normality under mild conditions. Further, we establish that the population version of the optimization criterion employed in Vuffray et al. (2019) can be interpreted as local maximum likelihood estimation (MLE). As part of our analysis, we introduce a robust variation of sparse linear regression a` la Lasso, which may be of interest in its own right.

Deep reinforcement learning has recently shown many impressive successes. However, one major obstacle towards applying such methods to real-world problems is their lack of data-efficiency. To this end, we propose the Bottleneck Simulator: a model-based reinforcement learning method which combines a learned, factorized transition model of the environment with rollout simulations to learn an effective policy from few examples. The learned transition model employs an abstract, discrete (bottleneck) state, which increases sample efficiency by reducing the number of model parameters and by exploiting structural properties of the environment. We provide a mathematical analysis of the Bottleneck Simulator in terms of fixed points of the learned policy, which reveals how performance is affected by four distinct sources of error: an error related to the abstract space structure, an error related to the transition model estimation variance, an error related to the transition model estimation bias, and an error related to the transition model class bias. Finally, we evaluate the Bottleneck Simulator on two natural language processing tasks: a text adventure game and a real-world, complex dialogue response selection task.

In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil this dynamical requirement and provide a framework where the trend of the process can be expressed as a latent variable. In this paper, we modify these recent asymmetric hidden Markov models to have an asymmetric autoregressive component, allowing the model to choose the order of autoregression that maximizes its penalized likelihood for a given training set. Additionally, we show how inference, hidden states decoding and parameter learning must be adapted to fit the proposed model. Finally, we run experiments with synthetic and real data to show the capabilities of this new model.

Temporal difference learning with linear function approximation is a popular method to obtain a low-dimensional approximation of the value function of a policy in a Markov Decision Process. We give a new interpretation of this method in terms of a splitting of the gradient of an appropriately chosen function. As a consequence of this interpretation, convergence proofs for gradient descent can be applied almost verbatim to temporal difference learning. Beyond giving a new, fuller explanation of why temporal difference works, our interpretation also yields improved convergence times. We consider the setting with $1/\sqrt{T}$ step-size, where previous comparable finite-time convergence time bounds for temporal difference learning had the multiplicative factor $1/(1-\gamma)$ in front of the bound, with $\gamma$ being the discount factor. We show that a minor variation on TD learning which estimates the mean of the value function separately has a convergence time where $1/(1-\gamma)$ only multiplies an asymptotically negligible term.

Learning complex behaviors through interaction requires coordinated long-term planning. Random exploration and novelty search lack task-centric guidance and waste effort on non-informative interactions. Instead, decision making should target samples with the potential to optimize performance far into the future, while only reducing uncertainty where conducive to this objective. This paper presents latent optimistic value exploration (LOVE), a strategy that enables deep exploration through optimism in the face of uncertain long-term rewards. We combine finite horizon rollouts from a latent model with value function estimates to predict infinite horizon returns and recover associated uncertainty through ensembling. Policy training then proceeds on an upper confidence bound (UCB) objective to identify and select the interactions most promising to improve long-term performance. We apply LOVE to visual control tasks in continuous state-action spaces and demonstrate improved sample complexity on a selection of benchmarking tasks.