Modeling human-scene interactions (HSI) is essential for understanding and simulating everyday human behaviors. Recent approaches utilizing generative modeling have made progress in this domain; however, they are limited in controllability and flexibility for real-world applications. To address these challenges, we propose reformulating the HSI modeling problem as Scene-aware Motion In-betweening---a more tractable and practical task. We introduce SceneMI, a framework that supports several practical applications, including keyframe-guided character animation in 3D scenes and enhancing the motion quality of imperfect HSI data. SceneMI employs dual scene descriptors to comprehensively encode global and local scene context. Furthermore, our framework leverages the inherent denoising nature of diffusion models to generalize on noisy keyframes. Experimental results demonstrate SceneMI's effectiveness in scene-aware keyframe in-betweening and generalization to the real-world GIMO dataset, where motions and scenes are acquired by noisy IMU sensors and smartphones. We further showcase SceneMI's applicability in HSI reconstruction from monocular videos.
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Signed Graph Neural Networks (SGNNs) are widely adopted to analyze complex patterns in signed graphs with both positive and negative links. Given the noisy nature of real-world connections, the robustness of SGNN has also emerged as a pivotal research area. Under the supervision of empirical properties, graph structure learning has shown its robustness on signed graph representation learning, however, there remains a paucity of research investigating a robust SGNN with theoretical guidance. Inspired by the success of graph information bottleneck (GIB) in information extraction, we propose RIDGE, a novel framework for Robust sIgned graph learning through joint Denoising of Graph inputs and supervision targEts. Different from the basic GIB, we extend the GIB theory with the capability of target space denoising as the co-existence of noise in both input and target spaces. In instantiation, RIDGE effectively cleanses input data and supervision targets via a tractable objective function produced by reparameterization mechanism and variational approximation. We extensively validate our method on four prevalent signed graph datasets, and the results show that RIDGE clearly improves the robustness of popular SGNN models under various levels of noise.
Fair Clustering for Data Summarization: Improved Approximation Algorithms and Complexity Insights
PDF ↗Data summarization tasks are often modeled as k-clustering problems, where the goal is to choose k data points, called cluster centers, that best represent the dataset by minimizing a clustering objective. A popular objective is to minimize the maximum distance between any data point and its nearest center, which is formalized as the k-center problem. While in some applications all data points can be chosen as centers, in the general setting, centers must be chosen from a predefined subset of points, referred as facilities or suppliers; this is known as the k-supplier problem. In this work, we focus on fair data summarization modeled as the fair k-supplier problem, where data consists of several groups, and a minimum number of centers must be selected from each group while minimizing the k-supplier objective. The groups can be disjoint or overlapping, leading to two distinct problem variants each with different computational complexity. We present 3-approximation algorithms for both variants, improving the previously known factor of 5. For disjoint groups, our algorithm runs in polynomial time, while for overlapping groups, we present a fixed-parameter tractable algorithm, where the exponential runtime depends only on the number of groups and centers. We show that these approximation factors match the theoretical lower bounds, assuming standard complexity theory conjectures. Finally, using an open-source implementation, we demonstrate the scalability of our algorithms on large synthetic datasets and assess the price of fairness on real-world data, comparing solution quality with and without fairness constraints.
Do real-world hypergraphs obey any patterns? Are power laws fundamental in hypergraphs as they are in real-world graphs? What generator can reproduce these patterns? A hypergraph is a generalization of a conventional graph, and it consists of nodes and hyperedges, with each hyperedge joining any number of nodes. Hypergraphs are adept at representing group interactions where two or more entities interact simultaneously, such as collaborative research and group discussions. In a wide range of real-world hypergraphs, we discover power-law or log-logistic distributions in eight structural properties. To simulate these observed patterns, we introduce HyRec, a tractable and realistic generative model leveraging the Kronecker product. We mathematically demonstrate that HyRec accurately reproduces both the patterns we observed and typical evolutionary trends found in real-world hypergraphs. To fit the parameters of HyRec to large-scale hypergraphs, we design SingFit, a fast and space-efficient algorithm successfully applied to eleven real-world hypergraphs with up to one million nodes and hyperedges. This paper makes the following contributions: (a) Discoveries: we identify multiple patterns that real-world hypergraphs obey, (b) Model: we propose HyRec, a tractable and realistic model capable of reproducing real-world hypergraphs efficiently (spec., with fewer than 1,000 parameters) with the support of SingFit, and (c) Proofs: we prove that HyRec adheres to these patterns.
Predicting changes in binding free energy (ΔΔ G) is a vital task in protein engineering and protein-protein interaction (PPI) engineering for drug discovery. Previous works have observed a high correlation between ΔΔ G and entropy, using probabilities of biologically important objects such as side chain angles and residue identities to estimate ΔΔ G. However, estimating the full conformational distribution of a protein complex is generally considered intractable. In this work, we propose a new approach to ΔΔ G prediction that avoids this issue by instead leveraging energy-based models for estimating the probability of a complex's conformation. Specifically, we novelly decompose ΔΔ G into a sequence-based component estimated by an inverse folding model and a structure-based component estimated by an energy model. This decomposition is made tractable by assuming equilibrium between the bound and unbound states, allowing us to simplify the estimation of degeneracies associated with each state. Unlike previous deep learning-based methods, our method incorporates an energy-based physical inductive bias by connecting the often-used sequence log-odds ratio-based approach to ΔΔ G prediction with a new ΔΔ E term grounded in statistical mechanics. We demonstrate superiority over existing state-of-the-art structure and sequence-based deep learning methods in ΔΔ G prediction and antibody optimization against SARS-CoV-2.
In Deep Neural Networks (DNNs), manipulating gradients is central to various algorithms, including data subset selection and instance attribution. For better tractability, practitioners often resort to using only the gradients of the last layer as a heuristic, instead of the full gradient across all model parameters, which we show is detrimental due to the Support Vector Effect (SVE). We introduce SVE, a max-margin-like behavior in the last layer(s) of DNNs and employ it to thoroughly scrutinize prevalent data selection and attribution methods relying on last layer gradients. Our investigation exposes limitations in these techniques and not only provides explanations for previously observed pitfalls, like lack of diversity and temporal performance degradation, but also offers fresh insights, including the vulnerability of existing methods to basic poisoning attacks and the potential for competitive performance using much simpler alternatives. Based on insights from SVE, we craft new methods RandE and PAE for data subset selection and instance attribution, respectively, which often outperform the purported state-of-the-art at a fraction of the cost, emphasizing the practical advantages of more efficient and less complex approaches.
Towards a Practical Tool for Music Composition: Using Constraint Programming to Model Chord Progressions and Modulations
PDF ↗The Harmoniser project aims to provide a practical tool to aid music composers in creating complete musical works. In this paper, we present a formal model of its second layer, tonal chord progressions and modulations to neighbouring tonalities, and a practical implementation using the Gecode constraint solver. Since music composition is too complex to formalize in its entirety, the Harmoniser project makes two assumptions for tractability: first, it focuses on tonal music (the basis of Western classical and popular music); second, it defines a simplified four-layer composition process that is relevant for a significant number of composers. Previous work on using constraint programming for music composition was limited to exploring the formalisation of different musical aspects and did not address the overall problem of building a practical composer tool. Harmoniser's four layers are global structure (tonal development of the whole piece), chord progressions (diatonic and chromatic) and modulations, voicing (four-voice chord layout), and ornaments (e.g., passing notes, appoggiaturas), all allowing iterative refinement by the composer. This paper builds on prior work for voicing layer 3, Diatony, and presents a model for layer 2, chord progressions and modulations. The results of the present paper can be used as input to Diatony to generate voicing. Future work will define models for the remaining layers, and combine all layers together with a graphical user interface as a plug-in for a DAW.
Probabilistic relational models such as parametric factor graphs enable efficient (lifted) inference by exploiting the indistinguishability of objects. In lifted inference, a representative of indistinguishable objects is used for computations. To obtain a relational (i.e., lifted) representation, the Advanced Colour Passing (ACP) algorithm is the state of the art. The ACP algorithm, however, requires underlying distributions, encoded as potential-based factorisations, to exactly match to identify and exploit indistinguishabilities. Hence, ACP is unsuitable for practical applications where potentials learned from data inevitably deviate even if associated objects are indistinguishable. To mitigate this problem, we introduce the ε-Advanced Colour Passing (ε-ACP) algorithm, which allows for a deviation of potentials depending on a hyperparameter ε. ε-ACP efficiently uncovers and exploits indistinguishabilities that are not exact. We prove that the approximation error induced by ε-ACP is strictly bounded and our experiments show that the approximation error is close to zero in practice.
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational problem posed by reasoning. Inspired by human reasoning, we introduce a method of first-order relational probabilistic inference that satisfies both criteria, and can handle hybrid (discrete and continuous) variables. Specifically, we extend sum-of-squares logic of expectation to relational settings, demonstrating that lifted reasoning in the bounded-degree fragment for knowledge bases of bounded quantifier rank can be performed in polynomial time, even with an a priori unknown and/or countably infinite set of objects. Crucially, our notion of tractability is framed in proof-theoretic terms, which extends beyond the syntactic properties of the language or queries. We are able to derive the tightest bounds provable by proofs of a given degree and size and establish completeness in our sum-of-squares refutations for fixed degrees.
Partially observable Markov decision processes (POMDPs) model specific environments in sequential decision-making under uncertainty. Critically, optimal policies for POMDPs may not be robust against perturbations in the environment. Hidden-model POMDPs (HM-POMDPs) capture sets of different environment models, that is, POMDPs with a shared action and observation space. The intuition is that the true model is hidden among a set of potential models, and it is unknown which model will be the environment at execution time. A policy is robust for a given HM-POMDP if it achieves sufficient performance for each of its POMDPs. We compute such robust policies by combining two orthogonal techniques: (1) a deductive formal verification technique that supports tractable robust policy evaluation by computing a worst-case POMDP within the HM-POMDP, and (2) subgradient ascent to optimize the candidate policy for a worst-case POMDP. The empirical evaluation shows that, compared to various baselines, our approach (1) produces policies that are more robust and generalize better to unseen POMDPs, and (2) scales to HM-POMDPs that consist of over a hundred thousand environments.
Optimal Transport on Categorical Data for Conterfactuals Using Compositional Data and Dirichlet Transport
PDF ↗Recently, optimal transport-based approaches have gained attention for deriving counterfactuals, e.g., to quantify algorithmic discrimination. However, in the general multivariate setting, these methods are often opaque and difficult to interpret. To address this, alternative methodologies have been proposed, using causal graphs combined with iterative quantile regressions or sequential transport to examine fairness at the individual level, often referred to as "counterfactual fairness." Despite these advancements, transporting categorical variables remains a significant challenge in practical applications with real datasets. In this paper, we propose a novel approach to address this issue. Our method involves (1) converting categorical variables into compositional data and (2) transporting these compositions within the probabilistic simplex of the Euclidean space. We demonstrate the applicability and effectiveness of this approach through an illustration on real-world data, and discuss limitations.
Boolean circuits in d-DNNF (determinstic Decomposable Negation Normal Form) enable tractable probabilistic inference, motivating research into compilers that transform arbitrary Boolean circuit into this form. However, d-DNNF compilers commonly require the input to be in conjunctive normal form (CNF), which means that a user must first convert their Boolean circuit into CNF. In this work, we argue that d-DNNF compilation would substantially benefit from reasoning over the original input circuit's structure, rather than solely relying on its CNF representation. To this end, we adapt an existing compiler and implement an optimisation that becomes more readily available once we reason over the input circuit: the identification and elimination of don't care variables. We empirically demonstrate the effectiveness of this approach, achieving a significant improvement in both the number of solved instances and the size of the resulting circuits.
We propose a general framework for assessing the exposure of sensitive knowledge in policy-protected knowledge bases (KBs), where knowledge is represented as logical theories and data protection policies are defined declaratively using epistemic dependencies. The framework models scenarios in which confidential parts of the KB may be publicly known due to security breaches. We study two fundamental decision problems: determining whether the exposed knowledge violates the data protection policy (leakage), and whether there exists a secure view of the KB that complies with the policy. We analyze the computational complexity (specifically, data complexity) of these problems, focusing on the DL-Lite_R and EL_\bot Description Logics. Our findings show that, for DL-Lite_R with restricted forms of policy, both the problems can be efficiently solved through query rewriting methods. For EL_\bot, we establish conditions for tractable computational bounds. Our results highlight the potential of this framework for practical applications in confidentiality-preserving knowledge management.
We consider a spatial voting model where both candidates and voters are positioned in the d-dimensional Euclidean space, and each voter ranks candidates based on their proximity to the voter's ideal point. We focus on the scenario where the given information about the locations of the voters' ideal points is incomplete; for each dimension, only an interval of possible values is known. In this context, we investigate the computational complexity of determining the possible winners under positional scoring rules. Our results show that the possible winner problem in one dimension is solvable in polynomial time for all k-truncated voting rules with constant k. Moreover, for some scoring rules for which the possible winner problem is NP-complete, such as approval voting for any dimension or k-approval for two or more dimensions, we give an FPT algorithm parameterized by the number of candidates. Finally, we classify tractable and intractable settings of the em weighted possible winner problem in one dimension, and resolve the computational complexity of the weighted case for all two-valued positional scoring rules when d=1.
Probabilistic circuits are a unifying representation of functions as computation graphs of weighted sums and products. Their primary application is in probabilistic modeling, where circuits with non-negative weights (monotone circuits) can be used to represent and learn density/mass functions, with tractable marginal inference. Recently, it was proposed to instead represent densities as the square of the circuit function (squared circuits); this allows the use of negative weights while retaining tractability, and can be exponentially more expressive efficient than monotone circuits. Unfortunately, we show the reverse also holds, meaning that monotone circuits and squared circuits are incomparable in general. This raises the question of whether we can reconcile, and indeed improve upon the two modeling approaches. We answer in the positive by proposing Inception PCs, a novel type of circuit that naturally encompasses both monotone circuits and squared circuits as special cases, and employs complex parameters. Empirically, we validate that Inception PCs can outperform both monotone and squared circuits on a range of tabular and image datasets.
Algebraic model counting unifies many inference tasks on logic formulas by exploiting semirings. Rather than focusing on inference, we consider learning, especially in statistical-relational and neurosymbolic AI, which combine logical, probabilistic and neural representations. Concretely, we show that the very same semiring perspective of algebraic model counting also applies to learning. This allows us to unify various learning algorithms by generalizing gradients and backpropagation to different semirings. Furthermore, we show how cancellation and ordering properties of a semiring can be exploited for more memory-efficient backpropagation. This allows us to obtain some interesting variations of state-of-the-art gradient-based optimisation methods for probabilistic logical models. We also discuss why algebraic model counting on tractable circuits does not lead to more efficient second-order optimization. Empirically, our algebraic backpropagation exhibits considerable speed-ups as compared to existing approaches.
Designing expressive generative models that support exact and efficient inference is a core question in probabilistic ML. Probabilistic circuits (PCs) offer a framework where this tractability-vs-expressiveness trade-off can be analyzed theoretically. Recently, squared PCs encoding subtractive mixtures via negative parameters have emerged as tractable models that can be exponentially more expressive than monotonic PCs, i.e., PCs with positive parameters only. In this paper we provide a more precise theoretical characterization of the expressiveness relationships among these models. First, we prove that squared PCs can be less expressive than monotonic ones. Second, we formalize a novel class of PCs – sum of squares PCs – that can be exponentially more expressive than both squared and monotonic PCs. Around sum of squares PCs, we build an expressiveness hierarchy that allows us to precisely unify and separate different tractable model classes such as Born Machines and PSD models, and other recently introduced tractable probabilistic models by using complex parameters. Finally, we empirically show the effectiveness of sum of squares circuits in performing distribution estimation.
SHAP scores represent the proposed use of the well-known Shapley values in eXplainable Artificial Intelligence (XAI). Recent work has shown that the exact computation of SHAP scores can produce unsatisfactory results. Concretely, for some ML models, SHAP scores will mislead with respect to relative feature influence. To address these limitations, recently proposed alternatives exploit different axiomatic aggregations, all of which are defined in terms of abductive explanations. However, the proposed axiomatic aggregations are not Shapley values. This paper investigates how SHAP scores can be modified so as to extend axiomatic aggregations to the case of Shapley values in XAI. More importantly, the proposed new definition of SHAP scores avoids all the known cases where unsatisfactory results have been identified. The paper also characterizes the complexity of computing the novel definition of SHAP scores, highlighting families of classifiers for which computing these scores is tractable. Furthermore, the paper proposes modifications to the existing implementations of SHAP scores. These modifications eliminate some of the known limitations of SHAP scores, and have negligible impact in terms of performance.
The independence assumption between random variables is a useful tool to increase the tractability of a modelling framework. However, this assumption can be too simplistic; failing to take dependencies into account can cause models to fail dramatically. The field of multi-axis graphical modelling (also called multi-way modelling, Kronecker-separable modelling) has seen growth over the past decade, but these models require that the data have zero mean. In the multi-axis case, inference is typically done in the single sample scenario, making mean inference impossible. In this paper, we demonstrate how the zero-mean assumption can cause egregious modelling errors for Kronecker-sum-decomposable Gaussian graphical models, as well as propose a relaxation to the zero-mean assumption that allows the avoidance of such errors. Specifically, we propose the "Kronecker-sum-structured mean" assumption, which leads to models with nonconvex-but-unimodal log-likelihoods that can be solved efficiently with coordinate descent.
An Algebraic Notion of Conditional Independence, and Its Application to Knowledge Representation
PDF ↗Conditional independence is a crucial concept supporting adequate modelling and efficient reasoning in probabilistics. In knowledge representation, the idea of conditional independence has also been introduced for specific formalisms, such as propositional logic and belief revision. In this paper, the notion of conditional independence is studied in the algebraic framework of approximation fixpoint theory. This gives a language-independent account of conditional independence that can be straightforwardly applied to any logic with fixpoint semantics. It is shown how this notion allows to reduce global reasoning to parallel instances of local reasoning, leading to fixed-parameter tractability results. Furthermore, relations to existing notions of conditional independence are discussed and the framework is applied to normal logic programming.