46 research outputs found
Causal Discovery from Temporal Data: An Overview and New Perspectives
Temporal data, representing chronological observations of complex systems,
has always been a typical data structure that can be widely generated by many
domains, such as industry, medicine and finance. Analyzing this type of data is
extremely valuable for various applications. Thus, different temporal data
analysis tasks, eg, classification, clustering and prediction, have been
proposed in the past decades. Among them, causal discovery, learning the causal
relations from temporal data, is considered an interesting yet critical task
and has attracted much research attention. Existing casual discovery works can
be divided into two highly correlated categories according to whether the
temporal data is calibrated, ie, multivariate time series casual discovery, and
event sequence casual discovery. However, most previous surveys are only
focused on the time series casual discovery and ignore the second category. In
this paper, we specify the correlation between the two categories and provide a
systematical overview of existing solutions. Furthermore, we provide public
datasets, evaluation metrics and new perspectives for temporal data casual
discovery.Comment: 52 pages, 6 figure
Distributional Actor-Critic Ensemble for Uncertainty-Aware Continuous Control
Uncertainty quantification is one of the central challenges for machine
learning in real-world applications. In reinforcement learning, an agent
confronts two kinds of uncertainty, called epistemic uncertainty and aleatoric
uncertainty. Disentangling and evaluating these uncertainties simultaneously
stands a chance of improving the agent's final performance, accelerating
training, and facilitating quality assurance after deployment. In this work, we
propose an uncertainty-aware reinforcement learning algorithm for continuous
control tasks that extends the Deep Deterministic Policy Gradient algorithm
(DDPG). It exploits epistemic uncertainty to accelerate exploration and
aleatoric uncertainty to learn a risk-sensitive policy. We conduct numerical
experiments showing that our variant of DDPG outperforms vanilla DDPG without
uncertainty estimation in benchmark tasks on robotic control and power-grid
optimization.Comment: 10 pages, 6 figures. Accepted to International Joint Conference on
Neural Networks (IJCNN 2022), July 18-23, Padua, Ital
The Poisson transform for unnormalised statistical models
Contrary to standard statistical models, unnormalised statistical models only
specify the likelihood function up to a constant. While such models are natural
and popular, the lack of normalisation makes inference much more difficult.
Here we show that inferring the parameters of a unnormalised model on a space
can be mapped onto an equivalent problem of estimating the intensity
of a Poisson point process on . The unnormalised statistical model now
specifies an intensity function that does not need to be normalised.
Effectively, the normalisation constant may now be inferred as just another
parameter, at no loss of information. The result can be extended to cover
non-IID models, which includes for example unnormalised models for sequences of
graphs (dynamical graphs), or for sequences of binary vectors. As a
consequence, we prove that unnormalised parameteric inference in non-IID models
can be turned into a semi-parametric estimation problem. Moreover, we show that
the noise-contrastive divergence of Gutmann & Hyv\"arinen (2012) can be
understood as an approximation of the Poisson transform, and extended to
non-IID settings. We use our results to fit spatial Markov chain models of eye
movements, where the Poisson transform allows us to turn a highly non-standard
model into vanilla semi-parametric logistic regression
Generalising weighted model counting
Given a formula in propositional or (finite-domain) first-order logic and some non-negative weights, weighted model counting (WMC) is a function problem that asks to compute the sum of the weights of the models of the formula. Originally used as a flexible way of performing probabilistic inference on graphical models, WMC has found many applications across artificial intelligence (AI), machine learning, and other domains. Areas of AI that rely on WMC include explainable AI, neural-symbolic AI, probabilistic programming, and statistical relational AI. WMC also has applications in bioinformatics, data mining, natural language processing, prognostics, and robotics.
In this work, we are interested in revisiting the foundations of WMC and considering generalisations of some of the key definitions in the interest of conceptual clarity and practical efficiency. We begin by developing a measure-theoretic perspective on WMC, which suggests a new and more general way of defining the weights of an instance. This new representation can be as succinct as standard WMC but can also expand as needed to represent less-structured probability distributions. We demonstrate the performance benefits of the new format by developing a novel WMC encoding for Bayesian networks. We then show how existing WMC encodings for Bayesian networks can be transformed into this more general format and what conditions ensure that the transformation is correct (i.e., preserves the answer). Combining the strengths of the more flexible representation with the tricks used in existing encodings yields further efficiency improvements in Bayesian network probabilistic inference.
Next, we turn our attention to the first-order setting. Here, we argue that the capabilities of practical model counting algorithms are severely limited by their inability to perform arbitrary recursive computations. To enable arbitrary recursion, we relax the restrictions that typically accompany domain recursion and generalise circuits (used to express a solution to a model counting problem) to graphs that are allowed to have cycles. These improvements enable us to find efficient solutions to counting fundamental structures such as injections and bijections that were previously unsolvable by any available algorithm.
The second strand of this work is concerned with synthetic data generation. Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm’s superiority over another. However, benchmarks are often limited and fail to reveal differences among the algorithms. First, we show how random instances of probabilistic logic programs (that typically use WMC algorithms for inference) can be generated using constraint programming. We also introduce a new constraint to control the independence structure of the underlying probability distribution and provide a combinatorial argument for the correctness of the constraint model. This model allows us to, for the first time, experimentally investigate inference algorithms on more than just a handful of instances. Second, we introduce a random model for WMC instances with a parameter that influences primal treewidth—the parameter most commonly used to characterise the difficulty of an instance. We show that the easy-hard-easy pattern with respect to clause density is different for algorithms based on dynamic programming and algebraic decision diagrams than for all other solvers. We also demonstrate that all WMC algorithms scale exponentially with respect to primal treewidth, although at differing rates
Stochastic Wasserstein Barycenters
We present a stochastic algorithm to compute the barycenter of a set of
probability distributions under the Wasserstein metric from optimal transport.
Unlike previous approaches, our method extends to continuous input
distributions and allows the support of the barycenter to be adjusted in each
iteration. We tackle the problem without regularization, allowing us to recover
a sharp output whose support is contained within the support of the true
barycenter. We give examples where our algorithm recovers a more meaningful
barycenter than previous work. Our method is versatile and can be extended to
applications such as generating super samples from a given distribution and
recovering blue noise approximations.Comment: ICML 201
Uncertainty-sensitive reasoning for inferring sameAs facts in linked data
albakri2016aInternational audienceDiscovering whether or not two URIs described in Linked Data -- in the same or different RDF datasets -- refer to the same real-world entity is crucial for building applications that exploit the cross-referencing of open data. A major challenge in data interlinking is to design tools that effectively deal with incomplete and noisy data, and exploit uncertain knowledge. In this paper, we model data interlinking as a reasoning problem with uncertainty. We introduce a probabilistic framework for modelling and reasoning over uncertain RDF facts and rules that is based on the semantics of probabilistic Datalog. We have designed an algorithm, ProbFR, based on this framework. Experiments on real-world datasets have shown the usefulness and effectiveness of our approach for data linkage and disambiguation
Learning Adversarial Low-rank Markov Decision Processes with Unknown Transition and Full-information Feedback
In this work, we study the low-rank MDPs with adversarially changed losses in
the full-information feedback setting. In particular, the unknown transition
probability kernel admits a low-rank matrix decomposition \citep{REPUCB22}, and
the loss functions may change adversarially but are revealed to the learner at
the end of each episode. We propose a policy optimization-based algorithm POLO,
and we prove that it attains the
regret
guarantee, where is rank of the transition kernel (and hence the dimension
of the unknown representations), is the cardinality of the action space,
is the cardinality of the model class, and is the discounted
factor. Notably, our algorithm is oracle-efficient and has a regret guarantee
with no dependence on the size of potentially arbitrarily large state space.
Furthermore, we also prove an
regret lower bound for this problem, showing that low-rank MDPs are
statistically more difficult to learn than linear MDPs in the regret
minimization setting. To the best of our knowledge, we present the first
algorithm that interleaves representation learning, exploration, and
exploitation to achieve the sublinear regret guarantee for RL with nonlinear
function approximation and adversarial losses
Graphical Models and Symmetries : Loopy Belief Propagation Approaches
Whenever a person or an automated system has to reason in uncertain domains, probability theory is necessary. Probabilistic graphical models allow us to build statistical models that capture complex dependencies between random variables. Inference in these models, however, can easily become intractable. Typical ways to address this scaling issue are inference by approximate message-passing, stochastic gradients, and MapReduce, among others. Exploiting the symmetries of graphical models, however, has not yet been considered for scaling statistical machine learning applications. One instance of graphical models that are inherently symmetric are statistical relational models. These have recently gained attraction within the machine learning and AI communities and combine probability theory with first-order logic, thereby allowing for an efficient representation of structured relational domains. The provided formalisms to compactly represent complex real-world domains enable us to effectively describe large problem instances. Inference within and training of graphical models, however, have not been able to keep pace with the increased representational power. This thesis tackles two major aspects of graphical models and shows that both inference and training can indeed benefit from exploiting symmetries. It first deals with efficient inference exploiting symmetries in graphical models for various query types. We introduce lifted loopy belief propagation (lifted LBP), the first lifted parallel inference approach for relational as well as propositional graphical models. Lifted LBP can effectively speed up marginal inference, but cannot straightforwardly be applied to other types of queries. Thus we also demonstrate efficient lifted algorithms for MAP inference and higher order marginals, as well as the efficient handling of multiple inference tasks. Then we turn to the training of graphical models and introduce the first lifted online training for relational models. Our training procedure and the MapReduce lifting for loopy belief propagation combine lifting with the traditional statistical approaches to scaling, thereby bridging the gap between statistical relational learning and traditional statistical machine learning