AISTATS 2020 Papers

Activity recognition in wearable computing faces two key challenges: i) activity characteristics may be context-dependent and change under different contexts or situations; ii) unknown contexts and activities may occur from time to time, requiring flexibility and adaptability of the algorithm. We develop a context-aware mixture of deep models termed the $\alpha$-$\beta$ network coupled with uncertainty quantification (UQ) based upon maximum entropy to enhance human activity recognition performance. We improve accuracy and F score by 10% by identifying high-level contexts in a data-driven way to guide model development. In order to ensure training stability, we have used a clustering-based pre-training in both public and in-house datasets, demonstrating improved accuracy through unknown context discovery.

We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are consistent and asymptotically control the type-1 error rate. Their test statistics can be evaluated in linear time (in the sample size). Suitable data representations are obtained in a data-driven way, by solving a supervised or unsupervised transfer-learning task on an auxiliary (potentially distinct) data set. If no auxiliary data is available, we split the data into two chunks: one for learning representations and one for computing the test statistic. In experiments on audio samples, natural images and three-dimensional neuroimaging data our tests yield significant decreases in type-2 error rate (up to 35 percentage points) compared to state-of-the-art two-sample tests such as kernel-methods and classifier two-sample tests.

We consider Inverse Reinforcement Learning (IRL) about multiple intentions, \ie the problem of estimating the unknown reward functions optimized by a group of experts that demonstrate optimal behaviors. Most of the existing algorithms either require access to a model of the environment or need to repeatedly compute the optimal policies for the hypothesized rewards. However, these requirements are rarely met in real-world applications, in which interacting with the environment can be expensive or even dangerous. In this paper, we address the IRL about multiple intentions in a fully model-free and batch setting. We first cast the single IRL problem as a constrained likelihood maximization and then we use this formulation to cluster agents based on the likelihood of the assignment. In this way, we can efficiently solve, without interactions with the environment, both the IRL and the clustering problem. Finally, we evaluate the proposed methodology on simulated domains and on a real-world social-network application.

N-gram models remain a fundamental component of language modeling. In data-scarce regimes, they are a strong alternative to neural models. Even when not used as-is, recent work shows they can regularize neural models. Despite this success, the effectiveness of one of the best N-gram smoothing methods, the one suggested by Kneser and Ney (1995), is not fully understood. In the hopes of explaining this performance, we study it through the lens of competitive distribution estimation: the ability to perform as well as an oracle aware of further structure in the data. We first establish basic competitive properties of Kneser-Ney smoothing. We then investigate the nature of its backoff mechanism and show that it emerges from first principles, rather than being an assumption of the model. We do this by generalizing the Good-Turing estimator to the contextual setting. This exploration leads us to a powerful generalization of Kneser-Ney, which we conjecture to have even stronger competitive properties. Empirically, it significantly improves performance on language modeling, even matching feed-forward neural models. To show that the mechanisms at play are not restricted to language modeling, we demonstrate similar gains on the task of predicting attack types in the Global Terrorism Database.

We provide a new analysis of local SGD, removing unnecessary assumptions and elaborating on the difference between two data regimes: identical and heterogeneous. In both cases, we improve the existing theory and provide values of the optimal stepsize and optimal number of local iterations. Our bounds are based on a new notion of variance that is specific to local SGD methods with different data. The tightness of our results is guaranteed by recovering known statements when we plug $H=1$, where $H$ is the number of local steps. The empirical evidence further validates the severe impact of data heterogeneity on the performance of local SGD.

We characterize the minimum noise amplitude and power for noise-adding mechanisms in (epsilon, delta)-differential privacy for single real-valued query function. We derive new lower bounds using the duality of linear programming, and new upper bounds by analyzing a special class of (epsilon, delta)-differentially private mechanisms, the truncated Laplacian mechanisms. We show that the multiplicative gap of the lower bounds and upper bounds goes to zero in various high privacy regimes, proving the tightness of the lower and upper bounds. In particular, our results close the previous constant multiplicative gap in the discrete setting. Numeric experiments show the improvement of the truncated Laplacian mechanism over the optimal Gaussian mechanism in all privacy regimes.

In this paper, we introduce a new online decision making paradigm that we call Thresholding Graph Bandits. The main goal is to efficiently identify a subset of arms in a multi-armed bandit problem whose means are above a specified threshold. While traditionally in such problems, the arms are assumed to be independent, in our paradigm we further suppose that we have access to the similarity between the arms in the form of a graph, allowing us to gain information about the arm means with fewer samples. Such a feature is particularly relevant in modern decision making problems, where rapid decisions need to be made in spite of the large number of options available. We present GrAPL, a novel algorithm for the thresholding graph bandit problem. We demonstrate theoretically that this algorithm is effective in taking advantage of the graph structure when the structure is reflective of the distribution of the rewards. We confirm these theoretical findings via experiments on both synthetic and real data.

The Thresholding Bandit Problem (TBP) aims to find the set of arms with mean rewards greater than a given threshold. We consider a new setting of TBP, where in addition to pulling arms, one can also duel two arms and get the arm with a greater mean. In our motivating application from crowdsourcing, dueling two arms can be more cost-effective and time-efficient than direct pulls. We refer to this problem as TBP with Dueling Choices (TBP-DC). This paper provides an algorithm called Rank-Search (RS) for solving TBP-DC by alternating between ranking and binary search. We prove theoretical guarantees for RS, and also give lower bounds to show the optimality of it. Experiments show that RS outperforms previous baseline algorithms that only use pulls or duels.

We address multi-armed bandits (MAB) where the objective is to maximize the cumulative reward under a probabilistic linear constraint. For a few real-world instances of this problem, constrained extensions of the well-known Thompson Sampling (TS) heuristic have recently been proposed. However, finite-time analysis of constrained TS is challenging; as a result, only O( sqrt( T ) ) bounds on the cumulative reward loss (i.e., the regret) are available. In this paper, we describe LinConTS, a TS-based algorithm for bandits that place a linear constraint on the probability of earning a reward in every round. We show that for LinConTS, the regret as well as the cumulative constraint violations are upper bounded by O( log ( T ) ). We develop a proof technique that relies on careful analysis of the dual problem and combine it with recent theoretical work on unconstrained TS. Through numerical experiments on two real-world datasets, we demonstrate that LinConTS outperforms an asymptotically optimal upper confidence bound (UCB) scheme in terms of simultaneously minimizing the regret and the violation.

We consider two multi-armed bandit problems with $n$ arms: \emph{(i)} given an $\epsilon > 0$, identify an arm with mean that is within $\epsilon$ of the largest mean and \emph{(ii)} given a threshold $\mu_0$ and integer $k$, identify $k$ arms with means larger than $\mu_0$. Existing lower bounds and algorithms for the PAC framework suggest that both of these problems require $\Omega(n)$ samples. However, we argue that the PAC framework not only conflicts with how these algorithms are used in practice, but also that these results disagree with intuition that says \emph{(i)} requires only $\Theta(\frac{n}{m})$ samples where $m = |\{ i : \mu_i > \max_{j \in [n]} \mu_j - \epsilon\}|$ and \emph{(ii)} requires $\Theta(\frac{n}{m}k)$ samples where $m = |\{ i : \mu_i > \mu_0 \}|$. We provide definitions that formalize these intuitions, obtain lower bounds that match the above sample complexities, and develop explicit, practical algorithms that achieve nearly matching upper bounds.

This paper introduces the Sylvester graphical lasso (SyGlasso) that captures multiway dependencies present in tensor-valued data. The model is based on the Sylvester equation that defines a generative model. The proposed model complements the tensor graphical lasso (Greenewald et al., 2019) that imposes a Kronecker sum model for the inverse covariance matrix, by providing an alternative Kronecker sum model that is generative and interpretable. A nodewise regression approach is adopted for estimating the conditional independence relationships among variables. The statistical convergence of the method is established, and empirical studies are provided to demonstrate the recovery of meaningful conditional dependency graphs. We apply the SyGlasso to an electroencephalography (EEG) study to compare the brain connectivity of alcoholic and nonalcoholic subjects. We demonstrate that our model can simultaneously estimate both the brain connectivity and its temporal dependencies.

We introduce the Quantile Snapshot Scan (Qsnap), a spatial scan algorithm which identifies spatial regions that differ the most between two snapshots in time. Qsnap is designed for spatial data with a numeric response and a vector of associated covariates for each spatial data point. Qsnap focuses on differences involving a specific quantile of the data distribution. A naive implementation of Qsnap is too computationally expensive for large datasets but our novel incremental update provides an order of magnitude speedup. We demonstrate Qsnap’s effectiveness over an extensive set of experiments on simulated data. In addition, we apply Qsnap to two real-world problems: discovering bird migration paths and identifying regions with dramatic changes in drought conditions.

One important partition of algorithms for controlling the false discovery rate (FDR) in multiple testing is into offline and online algorithms. The first generally achieve significantly higher power of discovery, while the latter allow making decisions sequentially as well as adaptively formulating hypotheses based on past observations. Using existing methodology, it is unclear how one could trade off the benefits of these two broad families of algorithms, all the while preserving their formal FDR guarantees. To this end, we introduce Batch-BH and Batch-St-BH, algorithms for controlling the FDR when a possibly infinite sequence of batches of hypotheses is tested by repeated application of one of the most widely used offline algorithms, the Benjamini-Hochberg (BH) method or Storey’s improvement of the BH method. We show that our algorithms interpolate between existing online and offline methodology, thus trading off the best of both worlds.

Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the ever-popular random forest, yet the nature of the subsampling effect, particularly of the features, is not well understood. We study the case of an ensemble of linear predictors, where each individual predictor is fit using ordinary least squares on a random submatrix of the data matrix. We show that, under standard Gaussianity assumptions, when the number of features selected for each predictor is optimally tuned, the asymptotic risk of a large ensemble is equal to the asymptotic ridge regression risk, which is known to be optimal among linear predictors in this setting. In addition to eliciting this implicit regularization that results from subsampling, we also connect this ensemble to the dropout technique used in training deep (neural) networks, another strategy that has been shown to have a ridge-like regularizing effect.

We consider a decentralized multi-agent Multi Armed Bandit (MAB) setup consisting of $N$ agents, solving the same MAB instance to minimize individual cumulative regret. In our model, agents collaborate by exchanging messages through pairwise gossip style communications. We develop two novel algorithms, where each agent only plays from a subset of all the arms. Agents use the communication medium to recommend only arm-IDs (not samples), and thus update the set of arms from which they play. We establish that, if agents communicate $\Omega(\log(T))$ times through any connected pairwise gossip mechanism, then every agent’s regret is a factor of order $N$ smaller compared to the case of no collaborations. Furthermore, we show that the communication constraints only have a second order effect on the regret of our algorithm. We then analyze this second order term of the regret to derive bounds on the regret-communication tradeoffs. Finally, we empirically evaluate our algorithm and conclude that the insights are fundamental and not artifacts of our bounds. We also show a lower bound which gives that the regret scaling obtained by our algorithm cannot be improved even in the absence of any communication constraints. Our results demonstrate that even a minimal level of collaboration among agents greatly reduces regret for all agents.

This paper introduces a new algorithm for the fundamental problem of generating a random integer from a discrete probability distribution using a source of independent and unbiased random coin flips. We prove that this algorithm, which we call the Fast Loaded Dice Roller (FLDR), is highly efficient in both space and time: (i) the size of the sampler is guaranteed to be linear in the number of bits needed to encode the input distribution; and (ii) the expected number of bits of entropy it consumes per sample is at most 6 bits more than the information-theoretically optimal rate. We present fast implementations of the linear-time preprocessing and near-optimal sampling algorithms using unsigned integer arithmetic. Empirical evaluations on a broad set of probability distributions establish that FLDR is 2x-10x faster in both preprocessing and sampling than multiple baseline algorithms, including the widely-used alias and interval samplers. It also uses up to 10000x less space than the information-theoretically optimal sampler, at the expense of less than 1.5x runtime overhead.

Normalizing flows have received a great deal of recent attention as they allow flexible generative modeling as well as easy likelihood computation. While a wide variety of flow models have been proposed, there is little formal understanding of the representation power of these models. In this work, we study some basic normalizing flows and rigorously establish bounds on their expressive power. Our results indicate that while these flows are highly expressive in one dimension, in higher dimensions their representation power may be limited, especially when the flows have moderate depth.

With the ubiquity of sensors in the IoT era, statistical observations are becoming increasingly available in the form of massive (multivariate) time-series. Formulated as unsupervised anomaly detection tasks, an abundance of applications like aviation safety management, the health monitoring of complex infrastructures or fraud detection can now rely on such functional data, acquired and stored with an ever finer granularity. The concept of \textit{statistical depth}, which reflects centrality of an arbitrary observation w.r.t. a statistical population may play a crucial role in this regard, anomalies corresponding to observations with ’small’ depth. Supported by sound theoretical and computational developments in the recent decades, it has proven to be extremely useful, in particular in functional spaces. However, most approaches documented in the literature consist in evaluating independently the centrality of each point forming the time series and consequently exhibit a certain insensitivity to possible shape changes.In this paper, we propose a novel notion of functional depth based on the area of the convex hull of sampled curves, capturing gradual departures from centrality, even beyond the envelope of the data, in a natural fashion.We discuss practical relevance of commonly imposed axioms on functional depths and investigate which of them are satisfied by the notion of depth we promote here. Estimation and computational issues are also adressed and various numerical experiments provide empirical evidence of the relevance of the approach proposed.

We introduce a novel random projection technique for efficiently reducing the dimension of very high-dimensional tensors. Building upon classical results on Gaussian random projections and Johnson-Lindenstrauss transforms (JLT), we propose two tensorized random projection maps relying on the tensor train (TT) and CP decomposition format, respectively. The two maps offer very low memory requirements and can be applied efficiently when the inputs are low rank tensors given in the CP or TT format.Our theoretical analysis shows that the dense Gaussian matrix in JLT can be replaced by a low-rank tensor implicitly represented in compressed form with random factors, while still approximately preserving the Euclidean distance of the projected inputs. In addition, our results reveal that the TT format is substantially superior to CP in terms of the size of the random projection needed to achieve the same distortion ratio. Experiments on synthetic data validate our theoretical analysis and demonstrate the superiority of the TT decomposition.