A body of recent work has focused on constructing a variational family of filtered distributions using Sequential Monte Carlo (SMC). Inspired by this work, we introduce Particle Smoothing Variational Objectives (SVO), a novel backward simulation technique and smoothed approximate posterior defined through a subsampling process. SVO augments support of the proposal and boosts particle diversity. Recent literature argues that increasing the number of samples K to obtain tighter variational bounds may hurt the proposal learning, due to a signal-to-noise ratio (SNR) of gradient estimators decreasing at the rate $\mathcal{O}(1/\sqrt{K})$. As a second contribution, we develop theoretical and empirical analysis of the SNR in filtering SMC, which motivates our choice of biased gradient estimators. We prove that introducing bias by dropping Categorical terms from the gradient estimate or using Gumbel-Softmax mitigates the adverse effect on the SNR. We apply SVO to three nonlinear latent dynamics tasks and provide statistics to rigorously quantify the predictions of filtered and smoothed objectives. SVO consistently outperforms filtered objectives when given fewer Monte Carlo samples on three nonlinear systems of increasing complexity.

Hierarchical clustering is a widely used approach for clustering datasets at multiple levels of granularity. Despite its popularity, existing algorithms such as hierarchical agglomerative clustering (HAC) are limited to the offline setting, and thus require the entire dataset to be available. This prohibits their use on large datasets commonly encountered in modern learning applications. In this paper, we consider hierarchical clustering in the online setting, where points arrive one at a time. We propose two algorithms that seek to optimize the Moseley and Wang (MW) revenue function, a variant of the Dasgupta cost. These algorithms offer different tradeoffs between efficiency and MW revenue performance. The first algorithm, OTD, is a highly efficient Online Top Down algorithm which provably achieves a 1/3-approximation to the MW revenue under a data separation assumption. The second algorithm, OHAC, is an online counterpart to offline HAC, which is known to yield a 1/3-approximation to the MW revenue, and produce good quality clusters in practice. We show that OHAC approximates offline HAC by leveraging a novel split-merge procedure. We empirically show that OTD and OHAC offer significant efficiency and cluster quality gains respectively over baselines.

Sepsis is the leading cause of death in non-coronary intensive care units. Moreover, a delay of antibiotic treatment of patients with severe sepsis by only few hours is associated with increased mortality. This insight makes accurate models for early prediction of sepsis a key task in machine learning for healthcare. Previous approaches have achieved high AUROC by learning from electronic health records where sepsis labels were defined automatically following established clinical criteria. We argue that the practice of incorporating the clinical criteria that are used to automatically define ground truth sepsis labels as features of severity scoring models is inherently circular and compromises the validity of the proposed approaches. We propose to create an independent ground truth for sepsis research by exploiting implicit knowledge of clinical practitioners via an electronic questionnaire which records attending physicians' daily judgements of patients' sepsis status. We show that despite its small size, our dataset allows to achieve state-of-the-art AUROC scores. An inspection of learned weights for standardized features of the linear model lets us infer potentially surprising feature contributions and allows to interpret seemingly counterintuitive findings.

Algorithms based on the entropy regularized framework, such as Soft Q-learning and Soft Actor-Critic, recently showed state-of-the-art performance on a number of challenging reinforcement learning (RL) tasks. The regularized formulation modifies the standard RL objective and thus, generally, converges to a policy different from the optimal greedy policy of the original RL problem. Practically, it is important to control the suboptimality of the regularized optimal policy. In this paper, we propose the optimality-preserving regularized modified policy iteration (MPI) scheme that simultaneously (a) provides desirable properties to intermediate policies such as targeted exploration, and (b) guarantees convergence to the optimal policy with explicit rates depending on the decrease rate of the regularization parameter. This result is based on two more general results. First, we show that the approximate MPI scheme converges as fast as the exact MPI if the decrease rate of error sequence is sufficiently fast; otherwise, its rate of convergence slows down to the errors decrease rate. Second, we show the regularized MPI is an instance of the approximate MPI where regularization plays the role of errors. In a special case of negative entropy regularizer (leading to a popular Soft Q-learning algorithm), our result explicitly links the convergence rate of policy / value iterates to exploration.

We provide high probability sample complexity guarantees for non-parametric structure learning of tree-shaped graphical models whose nodes are discrete random variables with a finite or countable alphabet, both in the noiseless and noisy regimes. First, we introduce a new, fundamental quantity called the (noisy) information threshold, which arises naturally from the error analysis of the Chow-Liu algorithm and characterizes not only the sample complexity, but also the inherent impact of the noise on the structure learning task, without explicit assumptions on the distribution of the model. This allows us to present the first non-parametric, high-probability finite sample complexity bounds on tree-structure learning from potentially noise-corrupted data. In particular, for number of nodes $p$, success rate $1-\delta$, and a fixed value of the information threshold, our sample complexity bounds for exact structure recovery are of the order of $\mathcal{O}\big(\log^{1+\zeta} (p/\delta)\big) $, for all $\zeta>0$, for both noiseless and noisy settings. Subsequently, we apply our results on two classes of hidden models, namely, the $M$-ary erasure channel and the generalized symmetric channel, illustrating the usefulness and importance of our framework. As a byproduct of our analysis, this paper resolves the open problem of tree structure learning in the presence of non-identically distributed observation noise, providing explicit conditions on the convergence of the Chow-Liu algorithm under this setting as well.

The success of deep (reinforcement) learning systems crucially depends on the correct choice of hyperparameters which are notoriously sensitive and expensive to evaluate. Training these systems typically requires running iterative processes over multiple epochs or episodes. Traditional approaches only consider final performances of a hyperparameter although intermediate information from the learning curve is readily available. In this paper, we present a Bayesian optimization approach which exploits the iterative structure of learning algorithms for efficient hyperparameter tuning. First, we transform each training curve into a numeric score. Second, we selectively augment the data using the auxiliary information from the curve. This augmentation step enables modeling efficiency while preventing the ill-conditioned issue of Gaussian process covariance matrix happened when adding the whole curve. We demonstrate the efficiency of our algorithm by tuning hyperparameters for the training of deep reinforcement learning agents and convolutional neural networks. Our algorithm outperforms all existing baselines in identifying optimal hyperparameters in minimal time.

Practical reinforcement learning problems are often formulated as constrained Markov decision process (CMDP) problems, in which the agent has to maximize the expected return while satisfying a set of prescribed safety constraints. In this study, we propose a novel simulator-based method to approximately solve a CMDP problem without making any compromise on the safety constraints. We achieve this by decomposing the CMDP into a pair of MDPs; reconnaissance MDP and planning MDP. The purpose of reconnaissance MDP is to evaluate the set of actions that are safe, and the purpose of planning MDP is to maximize the return while using the actions authorized by reconnaissance MDP. RMDP can define a set of safe policies for any given set of safety constraint, and this set of safe policies can be used to solve another CMDP problem with different reward. Our method is not only computationally less demanding than the previous simulator-based approaches to CMDP, but also capable of finding a competitive reward-seeking policy in a high dimensional environment, including those involving multiple moving obstacles.

We introduce a framework to study the transformation of problems with manifold constraints into unconstrained problems through parametrizations in terms of a Euclidean space. We call these parametrizations "trivializations". We prove conditions under which a trivialization is sound in the context of gradient-based optimization and we show how two large families of trivializations have overall favorable properties, but also suffer from a performance issue. We then introduce "dynamic trivializations", which solve this problem, and we show how these form a family of optimization methods that lie between trivializations and Riemannian gradient descent, and combine the benefits of both of them. We then show how to implement these two families of trivializations in practice for different matrix manifolds. To this end, we prove a formula for the gradient of the exponential of matrices, which can be of practical interest on its own. Finally, we show how dynamic trivializations improve the performance of existing methods on standard tasks designed to test long-term memory within neural networks.

Furthermore it has provided theoretical certitude on the effectivness of the procedure. However, the iterative optimisation method associated with the diversity and flexibility of the architecture of a firing graph opens doors to further applications, notably in the field of inverse problem and in the very hype field of machine learning. Indeed in supervised classification, we are given a dataset composed of features that may be numerical or categorical description of samples and targets that specify the class of samples. If we assume that the activation of a target is a combination of latent factors's activations and that we operate the minimum transformation of features so that they take the form of a measure grid, a light layer of procedures could turn our solution into a supervised classificator. The specificity of such a learner would give it an interesting position in the supervised learning landscape. Indeed, its iterative optimisation and flexible architecture could make it an adaptative learner, that scale to large dataset, with minimum processing work on raw data, in the manner of a neural network. Yet unlike neural network the algorithm handle very efficiently categorical or sparse feature space. Furthermore, compared to the most advanced tree based classification, its flexible architecture is more suitable to learning update and on-the-fly evaluation or addition of new features. Finally, given the hype granted to the field of machine learning nowaday, both in the scientific comunity and civil society, it would be common sense to orient this piece of research to this field.

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies on judiciously combining a large number of computationally cheap training data on coarse resolutions with a few expensive training samples on fine grid resolutions. Theoretical arguments for lowering the generalization error, based on reducing the variance of the underlying maps, are provided and numerical evidence, indicating significant gains over underlying single-level machine learning algorithms, are presented. Moreover, we also apply the multi-level algorithm in the context of forward uncertainty quantification and observe a considerable speed-up over competing algorithms.