Data deletion algorithms aim to remove the influence of deleted data points from trained models at a cheaper computational cost than fully retraining those models. However, for sequences of deletions, most prior work in the non-convex setting gives valid guarantees only for sequences that are chosen independently of the models that are published. If people choose to delete their data as a function of the published models (because they don't like what the models reveal about them, for example), then the update sequence is adaptive. In this paper, we give a general reduction from deletion guarantees against adaptive sequences to deletion guarantees against non-adaptive sequences, using differential privacy and its connection to max information. Combined with ideas from prior work which give guarantees for non-adaptive deletion sequences, this leads to extremely flexible algorithms able to handle arbitrary model classes and training methodologies, giving strong provable deletion guarantees for adaptive deletion sequences. We show in theory how prior work for non-convex models fails against adaptive deletion sequences, and use this intuition to design a practical attack against the SISA algorithm of Bourtoule et al. [2021] on CIFAR-10, MNIST, Fashion-MNIST.
Network regression models, where the outcome comprises the valued edge in a network and the predictors are actor or dyad-level covariates, are used extensively in the social and biological sciences. Valid inference relies on accurately modeling the residual dependencies among the relations. Frequently homogeneity assumptions are placed on the errors which are commonly incorrect and ignore critical, natural clustering of the actors. In this work, we present a novel regression modeling framework that models the errors as resulting from a community-based dependence structure and exploits the subsequent exchangeability properties of the error distribution to obtain parsimonious standard errors for regression parameters.
Deep generative models have emerged as a powerful tool for learning useful molecular representations and designing novel molecules with desired properties, with applications in drug discovery and material design. However, most existing deep generative models are restricted due to lack of spatial information. Here we propose augmentation of deep generative models with topological data analysis (TDA) representations, known as persistence images, for robust encoding of 3D molecular geometry. We show that the TDA augmentation of a character-based Variational Auto-Encoder (VAE) outperforms state-of-the-art generative neural nets in accurately modeling the structural composition of the QM9 benchmark. Generated molecules are valid, novel, and diverse, while exhibiting distinct electronic property distribution, namely higher sample population with small HOMO-LUMO gap. These results demonstrate that TDA features indeed provide crucial geometric signal for learning abstract structures, which is non-trivial for existing generative models operating on string, graph, or 3D point sets to capture.
Calcium deficiency in high yielding bovines during calving causes milk fever which leads to economic losses of around INR 1000 crores (USD 137 million) per annum in Haryana, India. With increasing milk production, the risk of milk fever is continuously rising. In the context, we aim to address the most fundamental research question: What is the effect of a preventive health product (anionic mineral mixture (AMM)) on milk fever incidence, milk productivity and farmers income? In an effort to contribute to the scanty economic literature on effect of preventive measures on nutritional deficiency disorders in dairy animals, specifically, on AMM effects in India, this study uses a randomized controlled design to estimate internally valid estimates. Using data from 200 dairy farms, results indicate that milk fever incidence decreases from 21 per cent at baseline to 2 per cent in treated animals at follow-up. Further, AMM leads to a 12 per cent and 38 per cent increase in milk yield and farmers net income, respectively. Profits earned due to the prevention of milk fever [INR 16000 (USD 218.7)] overweighs the losses from milk fever [INR 4000 (USD 54.7)]; thus, prevention using AMM is better than cure.
Coordination between heat and electricity markets is essential to achieve a cost-effective and efficient operation of the overall energy system. In the current sequential market practice, the heat market is cleared before the electricity market, and has no insight into the impacts of heat dispatch on the electricity market. While preserving this sequential practice, this paper introduces an ``electricity-aware'' bid format for the coordination of heat and electricity systems. This novel market mechanism defines heat bids conditionally on day-ahead electricity prices. Prior to clearing heat and electricity markets, the proposed bid selection mechanism selects the ``valid'' bids which minimize the operating cost of the heat system, while anticipating heat and electricity market clearing.} This mechanism is modeled as a trilevel optimization problem, which we recast as a mixed-integer linear program using a lexicographic function. We use a realistic case study based on the Danish electricity and heat system, and show that the proposed bid selection mechanism yields a 4.5\% reduction in total operating cost of heat and electricity systems compared to the existing market-clearing procedure, while reducing the financial losses of combined heat and power plants and heat pumps due to invalid bids by up to 20.3 million euros.
Blockwise missing data occurs frequently when we integrate multisource or multimodality data where different sources or modalities contain complementary information. In this paper, we consider a high-dimensional linear regression model with blockwise missing covariates and a partially observed response variable. Under this framework, we propose a computationally efficient estimator for the regression coefficient vector based on carefully constructed unbiased estimating equations and a blockwise imputation procedure, and obtain its rate of convergence. Furthermore, building upon an innovative projected estimating equation technique that intrinsically achieves bias-correction of the initial estimator, we propose a nearly unbiased estimator for each individual regression coefficient, which is asymptotically normally distributed under mild conditions. Based on these debiased estimators, asymptotically valid confidence intervals and statistical tests about each regression coefficient are constructed. Numerical studies and application analysis of the Alzheimer's Disease Neuroimaging Initiative data show that the proposed method performs better and benefits more from unsupervised samples than existing methods.
Multiple different responses are often plausible for a given open domain dialog context. Prior work has shown the importance of having multiple valid reference responses for meaningful and robust automated evaluations. In such cases, common practice has been to collect more human written references. However, such collection can be expensive, time consuming, and not easily scalable. Instead, we propose a novel technique for automatically expanding a human generated reference to a set of candidate references. We fetch plausible references from knowledge sources, and adapt them so that they are more fluent in context of the dialog instance in question. More specifically, we use (1) a commonsense knowledge base to elicit a large number of plausible reactions given the dialog history (2) relevant instances retrieved from dialog corpus, using similar past as well as future contexts. We demonstrate that our automatically expanded reference sets lead to large improvements in correlations of automated metrics with human ratings of system outputs for DailyDialog dataset.
Fast and efficient sampling-based motion planning (SMP) is an integral component of many robotic systems, such as autonomous cars. A popular technique to improve the efficiency of these planners is to restrict search space in the planning domain. Existing algorithms define parametric functions to bound the search space, but these do not extend to non-holonomic robotic systems. Recent learning-based methods use a combination of convolutional and fully connected networks to encode the planning space. However, these methods are restricted to fixed map sizes, which are often not realistic in the real world. In this paper, we introduce a transformer-based approach, Motion Planning Transformer, to restrict the search space by learning to discern regions with a valid path from prior data. The model learns not only to restrict search spaces for simple 2D systems but also for non-holonomic robotic systems. We validate our method on various randomly generated environments with different map sizes and plan trajectories for a physical non-holonomic robot. We also provide a ROS2 plugin of our method for the Nav2 planning stack. The results show that our method reduces search space nodes by 2-12 times compared to traditional planners and has better generalizability than recent learning-based planners.
The distributional reinforcement learning (RL) approach advocates for representing the complete probability distribution of the random return instead of only modelling its expectation. A distributional RL algorithm may be characterised by two main components, namely the representation of the distribution together with its parameterisation and the probability metric defining the loss. The present research work considers the unconstrained monotonic neural network (UMNN) architecture, a universal approximator of continuous monotonic functions which is particularly well suited for modelling different representations of a distribution. This property enables the efficient decoupling of the effect of the function approximator class from that of the probability metric. The research paper firstly introduces a methodology for learning different representations of the random return distribution (PDF, CDF and QF). Secondly, a novel distributional RL algorithm named unconstrained monotonic deep Q-network (UMDQN) is presented. To the authors' knowledge, it is the first distributional RL method supporting the learning of three, valid and continuous representations of the random return distribution. Lastly, in light of this new algorithm, an empirical comparison is performed between three probability quasi-metrics, namely the Kullback-Leibler divergence, Cramer distance, and Wasserstein distance. The results highlight the main strengths and weaknesses associated with each probability metric together with an important limitation of the Wasserstein distance.
ResNets constrained to be bi-Lipschitz, that is, approximately distance preserving, have been a crucial component of recently proposed techniques for deterministic uncertainty quantification in neural models. We show that theoretical justifications for recent regularisation schemes trying to enforce such a constraint suffer from a crucial flaw -- the theoretical link between the regularisation scheme used and bi-Lipschitzness is only valid under conditions which do not hold in practice, rendering existing theory of limited use, despite the strong empirical performance of these models. We provide a theoretical explanation for the effectiveness of these regularisation schemes using a frequency analysis perspective, showing that under mild conditions these schemes will enforce a lower Lipschitz bound on the low-frequency projection of images. We then provide empirical evidence supporting our theoretical claims, and perform further experiments which demonstrate that our broader conclusions appear to hold when some of the mathematical assumptions of our proof are relaxed, corresponding to the setup used in prior work. In addition, we present a simple constructive algorithm to search for counter examples to the distance preservation condition, and discuss possible implications of our theory for future model design.
We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one into the other, such that after the rewrite the two programs are structurally identical, and therefore trivially equivalent.We then develop a graph-to-sequence neural network system for program equivalence, trained to produce such rewrite sequences from a carefully crafted automatic example generation algorithm. We extensively evaluate our system on a rich multi-type linear algebra expression language, using arbitrary combinations of 100+ graph-rewriting axioms of equivalence. Our machine learning system guarantees correctness for all true negatives, and ensures 0 false positive by design. It outputs via inference a valid proof of equivalence for 93% of the 10,000 equivalent expression pairs isolated for testing, using up to 50-term expressions. In all cases, the validity of the sequence produced and therefore the provable assertion of program equivalence is always computable, in negligible time.
Tyshkovskiy and Panchin have recently published a commentary on our paper in which they outline several "points of disagreement with the Segreto/Deigin hypothesis". As our paper is titled "The genetic structure of SARS-CoV-2 does not rule out a laboratory origin", points of disagreement should provide evidence that rules out a laboratory origin. However, Tyshkovskiy and Panchin provide no such evidence and instead attempt to criticize our arguments that highlight aspects of SARS-CoV-2 that could be consistent with the lab leak hypothesis. Strikingly, Tyshkovskiy and Panchin's main point of criticism is based on a false premise that we have claimed RaTG13 to be a direct progenitor of SARS-CoV-2, and their other points of criticism are either incorrect or irrelevant to our hypotheses. Thus, the genetic structure of SARS-CoV-2 remains consistent with both natural or laboratory origin, which means that both the zoonotic and the lab leak hypothesis need to be investigated equally thoroughly.
Dimensionality reduction (DR) and manifold learning (ManL) have been applied extensively in many machine learning tasks, including signal processing, speech recognition, and neuroinformatics. However, the understanding of whether DR and ManL models can generate valid learning results remains unclear. In this work, we investigate the validity of learning results of some widely used DR and ManL methods through the chart mapping function of a manifold. We identify a fundamental problem of these methods: the mapping functions induced by these methods violate the basic settings of manifolds, and hence they are not learning manifold in the mathematical sense. To address this problem, we provide a provably correct algorithm called fixed points Laplacian mapping (FPLM), that has the geometric guarantee to find a valid manifold representation (up to a homeomorphism). Combining one additional condition(orientation preserving), we discuss a sufficient condition for an algorithm to be bijective for any d-simplex decomposition result on a d-manifold. However, constructing such a mapping function and its computational method satisfying these conditions is still an open problem in mathematics.
Controlled feature selection aims to discover the features a response depends on while limiting the false discovery rate (FDR) to a predefined level. Recently, multiple deep-learning-based methods have been proposed to perform controlled feature selection through the Model-X knockoff framework. We demonstrate, however, that these methods often fail to control the FDR for two reasons. First, these methods often learn inaccurate models of features. Second, the "swap" property, which is required for knockoffs to be valid, is often not well enforced. We propose a new procedure called FlowSelect to perform controlled feature selection that does not suffer from either of these two problems. To more accurately model the features, FlowSelect uses normalizing flows, the state-of-the-art method for density estimation. Instead of enforcing the "swap" property, FlowSelect uses a novel MCMC-based procedure to calculate p-values for each feature directly. Asymptotically, FlowSelect computes valid p-values. Empirically, FlowSelect consistently controls the FDR on both synthetic and semi-synthetic benchmarks, whereas competing knockoff-based approaches do not. FlowSelect also demonstrates greater power on these benchmarks. Additionally, FlowSelect correctly infers the genetic variants associated with specific soybean traits from GWAS data.
Recently, there have been several papers that discuss the extension of the Pinball loss Support Vector Machine (Pin-SVM) model, originally proposed by Huang et al.,[1][2]. Pin-SVM classifier deals with the pinball loss function, which has been defined in terms of the parameter $\tau$. The parameter $\tau$ can take values in $[ -1,1]$. The existing Pin-SVM model requires to solve the same optimization problem for all values of $\tau$ in $[ -1,1]$. In this paper, we improve the existing Pin-SVM model for the binary classification task. At first, we note that there is major difficulty in Pin-SVM model (Huang et al. [1]) for $ -1 \leq \tau < 0$. Specifically, we show that the Pin-SVM model requires the solution of different optimization problem for $ -1 \leq \tau < 0$. We further propose a unified model termed as Unified Pin-SVM which results in a QPP valid for all $-1\leq \tau \leq 1$ and hence more convenient to use. The proposed Unified Pin-SVM model can obtain a significant improvement in accuracy over the existing Pin-SVM model which has also been empirically justified by extensive numerical experiments with real-world datasets.
Partial-label learning (PLL) generally focuses on inducing a noise-tolerant multi-class classifier by training on overly-annotated samples, each of which is annotated with a set of labels, but only one is the valid label. A basic promise of existing PLL solutions is that there are sufficient partial-label (PL) samples for training. However, it is more common than not to have just few PL samples at hand when dealing with new tasks. Furthermore, existing few-shot learning algorithms assume precise labels of the support set; as such, irrelevant labels may seriously mislead the meta-learner and thus lead to a compromised performance. How to enable PLL under a few-shot learning setting is an important problem, but not yet well studied. In this paper, we introduce an approach called FsPLL (Few-shot PLL). FsPLL first performs adaptive distance metric learning by an embedding network and rectifying prototypes on the tasks previously encountered. Next, it calculates the prototype of each class of a new task in the embedding network. An unseen example can then be classified via its distance to each prototype. Experimental results on widely-used few-shot datasets (Omniglot and miniImageNet) demonstrate that our FsPLL can achieve a superior performance than the state-of-the-art methods across different settings, and it needs fewer samples for quickly adapting to new tasks.
Contextual bandit algorithms are increasingly replacing non-adaptive A/B tests in e-commerce, healthcare, and policymaking because they can both improve outcomes for study participants and increase the chance of identifying good or even best policies. To support credible inference on novel interventions at the end of the study, nonetheless, we still want to construct valid confidence intervals on average treatment effects, subgroup effects, or value of new policies. The adaptive nature of the data collected by contextual bandit algorithms, however, makes this difficult: standard estimators are no longer asymptotically normally distributed and classic confidence intervals fail to provide correct coverage. While this has been addressed in non-contextual settings by using stabilized estimators, the contextual setting poses unique challenges that we tackle for the first time in this paper. We propose the Contextual Adaptive Doubly Robust (CADR) estimator, the first estimator for policy value that is asymptotically normal under contextual adaptive data collection. The main technical challenge in constructing CADR is designing adaptive and consistent conditional standard deviation estimators for stabilization. Extensive numerical experiments using 57 OpenML datasets demonstrate that confidence intervals based on CADR uniquely provide correct coverage.
We develop a method to generate prediction intervals that have a user-specified coverage level across all regions of feature-space, a property called conditional coverage. A typical approach to this task is to estimate the conditional quantiles with quantile regression -- it is well-known that this leads to correct coverage in the large-sample limit, although it may not be accurate in finite samples. We find in experiments that traditional quantile regression can have poor conditional coverage. To remedy this, we modify the loss function to promote independence between the size of the intervals and the indicator of a miscoverage event. For the true conditional quantiles, these two quantities are independent (orthogonal), so the modified loss function continues to be valid. Moreover, we empirically show that the modified loss function leads to improved conditional coverage, as evaluated by several metrics. We also introduce two new metrics that check conditional coverage by looking at the strength of the dependence between the interval size and the indicator of miscoverage.
Crucial for building trust in deep learning models for critical real-world applications is efficient and theoretically sound uncertainty quantification, a task that continues to be challenging. Useful uncertainty information is expected to have two key properties: It should be valid (guaranteeing coverage) and discriminative (more uncertain when the expected risk is high). Moreover, when combined with deep learning (DL) methods, it should be scalable and affect the DL model performance minimally. Most existing Bayesian methods lack frequentist coverage guarantees and usually affect model performance. The few available frequentist methods are rarely discriminative and/or violate coverage guarantees due to unrealistic assumptions. Moreover, many methods are expensive or require substantial modifications to the base neural network. Building upon recent advances in conformal prediction [13, 33] and leveraging the classical idea of kernel regression, we propose Locally Valid and Discriminative prediction intervals (LVD), a simple, efficient, and lightweight method to construct discriminative prediction intervals (PIs) for almost any DL model. With no assumptions on the data distribution, such PIs also offer finite-sample local coverage guarantees (contrasted to the simpler marginal coverage). We empirically verify, using diverse datasets, that besides being the only locally valid method for DL, LVD also exceeds or matches the performance (including coverage rate and prediction accuracy) of existing uncertainty quantification methods, while offering additional benefits in scalability and flexibility.
Decision-making under uncertainty is hugely important for any decisions sensitive to perturbations in observed data. One method of incorporating uncertainty into making optimal decisions is through robust optimization, which minimizes the worst-case scenario over some uncertainty set. We connect conformal prediction regions to robust optimization, providing finite sample valid and conservative ellipsoidal uncertainty sets, aptly named conformal uncertainty sets. In pursuit of this connection we explicitly define Mahalanobis distance as a potential conformity score in full conformal prediction. We also compare the coverage and optimization performance of conformal uncertainty sets, specifically generated with Mahalanobis distance, to traditional ellipsoidal uncertainty sets on a collection of simulated robust optimization examples.