Despite its wide use, recent studies have revealed unexpected and undesirable properties of neural autoregressive sequence models trained with maximum likelihood, such as an unreasonably high affinity to short sequences after training and to infinitely long sequences at decoding time. We propose to study these phenomena by investigating how the modes, or local maxima, of a distribution are maintained throughout the full learning chain of the ground-truth, empirical, learned and decoding-induced distributions, via the newly proposed mode recovery cost. We design a tractable testbed where we build three types of ground-truth distributions: (1) an LSTM based structured distribution, (2) an unstructured distribution where probability of a sequence does not depend on its content, and (3) a product of these two which we call a semi-structured distribution. Our study reveals both expected and unexpected findings. First, starting with data collection, mode recovery cost strongly relies on the ground-truth distribution and is most costly with the semi-structured distribution. Second, after learning, mode recovery cost from the ground-truth distribution may increase or decrease compared to data collection, with the largest cost degradation occurring with the semi-structured ground-truth distribution. Finally, the ability of the decoding-induced distribution to recover modes from the learned distribution is highly impacted by the choices made earlier in the learning chain. We conclude that future research must consider the entire learning chain in order to fully understand the potentials and perils and to further improve neural autoregressive sequence models.

Given a set of samples, the parameters of a GM are determined in such a way as to best fit the samples in a maximum likelihood way. Solutions for equally weighted samples are readily available, expectation-maximization (EM) based methods being the most prevalent because of low computational requirements and ease of implementation. So it comes as a surprise that GM estimation for weighted samples is hard to find in literature. It might be even more surprising that the standard reference [1] gives incorrect results, see Figure 1. 2. Context Applications for sample-to-density function approximation include clustering of unlabled data [2, 3], multi-target tracking [4, 5], group tracking [6], multilateration [7, 8], and arbitrary density representation in nonlinear filters [9, 10]. A popular basic solution to this is the k-means algorithm. It does not find a complete density representation, only the means of the individual clusters. The k-means algorithm uses hard sample-tomean associations, therefore yields merely approximate solutions but can be computationally optimized using k-d trees [11, 12]. Moreover, the global optimum can be found deterministically [13], therefore it can be used to provide an initial guess for more elaborate algorithms. A sample-to-density approximation that is optimal in a maximum likelihood sense can be searched with numerical optimization techniques such as the Newton algorithm that has quadratic convergence but high computational demand per iteration, quasi-Newton methods, the method of scoring, or the conjugate gradient method with slower convergence but less computational effort per iteration [14].

Model discovery aims at autonomously discovering differential equations underlying a dataset. Approaches based on Physics Informed Neural Networks (PINNs) have shown great promise, but a fully-differentiable model which explicitly learns the equation has remained elusive. In this paper we propose such an approach by combining neural network based surrogates with Sparse Bayesian Learning (SBL). We start by reinterpreting PINNs as multitask models, applying multitask learning using uncertainty, and show that this leads to a natural framework for including Bayesian regression techniques. We then construct a robust model discovery algorithm by using SBL, which we showcase on various datasets. Concurrently, the multitask approach allows the use of probabilistic approximators, and we show a proof of concept using normalizing flows to directly learn a density model from single particle data. Our work expands PINNs to various types of neural network architectures, and connects neural network-based surrogates to the rich field of Bayesian parameter inference.

Linear mixed models (LMM) (Laird and Ware, 1982) are widely used in longitudinal data analysis as they incorporate random effects to deal with group-specific heterogeneity. Data involving repeated observations of the same variables are common in epidemiology, medical statistics and many other fields. Likelihood-based methods are often used to make inference for (generalized) linear mixed models (Bates et al., 2000; Gumedze and Dunne, 2011). Schelldorfer et al. (2011) and Groll and Tutz (2014) introduced separately the L1-penalized estimation for high-dimensional linear mixed models. Fong et al. (2010) argued that for small sample sizes likelihood-based inference can be unreliable with variance components being difficult to estimate and suggested to use the Bayesian method. When the random effects distribution is misspecified, the resulting maximum likelihood estimators are inconsistent and biased (Neuhaus et al., 1992; Heagerty and Kurland, 2001; Litière et al., 2008). Fahrmeir and Lang (2001) presented a fully Bayesian inference via Markov Chain Monte Carlo (MCMC) simulation in generalized additive and semiparametric mixed models. Rosa et al. (2003) described a normal/independent residual distributions for robust inference and suggested also the Bayesian framework. Bayesian inference for mixed models can be conducted with for example BayesX, a program with MCMC simulation techniques (Lang and Brezger, 2000).

Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to three key hypotheses: parametric, linear and homogeneous. Recent work has attempted to address these limitations separately. This work aims to overcome all three assumptions simultaneously by proposing the flexible state-switching Hawkes processes: a flexible, nonlinear and nonhomogeneous variant where a state process is incorporated to interact with the point processes. The proposed model empowers Hawkes processes to be applied to time-varying systems. For inference, we utilize the latent variable augmentation technique to design two efficient Bayesian inference algorithms: Gibbs sampler and mean-field variational inference, with analytical iterative updates to estimate the posterior. In experiments, our model achieves superior performance compared to the state-of-the-art competitors.

The Hidden Markov Model or HMM is all about learning sequences. A lot of the data that would be very useful for us to model is in sequences. Stock prices are sequences of prices. Language is a sequence of words. Credit scoring involves sequences of borrowing and repaying money, and we can use those sequences to predict whether or not you're going to default.

Bayesian optimization (BO) conventionally relies on handcrafted acquisition functions (AFs) to sequentially determine the sample points. However, it has been widely observed in practice that the best-performing AF in terms of regret can vary significantly under different types of black-box functions. It has remained a challenge to design one AF that can attain the best performance over a wide variety of black-box functions. This paper aims to attack this challenge through the perspective of reinforced few-shot AF learning (FSAF). Specifically, we first connect the notion of AFs with Q-functions and view a deep Q-network (DQN) as a surrogate differentiable AF. While it serves as a natural idea to combine DQN and an existing few-shot learning method, we identify that such a direct combination does not perform well due to severe overfitting, which is particularly critical in BO due to the need of a versatile sampling policy. To address this, we present a Bayesian variant of DQN with the following three features: (i) It learns a distribution of Q-networks as AFs based on the Kullback-Leibler regularization framework. This inherently provides the uncertainty required in sampling for BO and mitigates overfitting. (ii) For the prior of the Bayesian DQN, we propose to use a demo policy induced by an off-the-shelf AF for better training stability. (iii) On the meta-level, we leverage the meta-loss of Bayesian model-agnostic meta-learning, which serves as a natural companion to the proposed FSAF. Moreover, with the proper design of the Q-networks, FSAF is general-purpose in that it is agnostic to the dimension and the cardinality of the input domain. Through extensive experiments, we demonstrate that the FSAF achieves comparable or better regrets than the state-of-the-art benchmarks on a wide variety of synthetic and real-world test functions.

Monte Carlo planners can often return sub-optimal actions, even if they are guaranteed to converge in the limit of infinite samples. Known asymptotic regret bounds do not provide any way to measure confidence of a recommended action at the conclusion of search. In this work, we prove bounds on the sub-optimality of Monte Carlo estimates for non-stationary bandits and Markov decision processes. These bounds can be directly computed at the conclusion of the search and do not require knowledge of the true action-value. The presented bound holds for general Monte Carlo solvers meeting mild convergence conditions. We empirically test the tightness of the bounds through experiments on a multi-armed bandit and a discrete Markov decision process for both a simple solver and Monte Carlo tree search.

We propose a safe DRL approach for autonomous vehicle (AV) navigation through crowds of pedestrians while making a left turn at an unsignalized intersection. Our method uses two long-short term memory (LSTM) models that are trained to generate the perceived state of the environment and the future trajectories of pedestrians given noisy observations of their movement. A future collision prediction algorithm based on the future trajectories of the ego vehicle and pedestrians is used to mask unsafe actions if the system predicts a collision. The performance of our approach is evaluated in two experiments using the high-fidelity CARLA simulation environment. The first experiment tests the performance of our method at intersections that are similar to the training intersection and the second experiment tests our method at intersections with a different topology. For both experiments, our methods do not result in a collision with a pedestrian while still navigating the intersection at a reasonable speed.

While classic control theory offers state of the art solutions in many problem scenarios, it is often desired to improve beyond the structure of such solutions and surpass their limitations. To this end, \emph{\gls{rpl}} offers a formulation to improve existing controllers with reinforcement learning (RL) by learning an additive "residual" to the output of a given controller. However, the applicability of such an approach highly depends on the structure of the controller. Often, internal feedback signals of the controller limit an RL algorithm to adequately change the policy and, hence, learn the task. We propose a new formulation that addresses these limitations by also modifying the feedback signals to the controller with an RL policy and show superior performance of our approach on a contact-rich peg-insertion task under position and orientation uncertainty. In addition, we use a recent impedance control architecture as control framework and show the difficulties of standard RPL. Furthermore, we introduce an adaptive curriculum for the given task to gradually increase the task difficulty in terms of position and orientation uncertainty. A video showing the results can be found at https://youtu.be/SAZm_Krze7U .