mlx

-module(mlx_causal).
-export([
    % Causal Discovery
    pc_algorithm/2, ges_algorithm/2, fast_causal_inference/2,
    causal_discovery_with_latents/2, constraint_based_discovery/3,
    score_based_discovery/3, hybrid_causal_discovery/3,
    
    % Causal Estimation
    instrumental_variables/3, regression_discontinuity/3,
    difference_in_differences/4, synthetic_control/4,
    causal_forests/4, double_ml/4, targeted_ml/4,
    
    % Causal Deep Learning
    causal_vae/3, causal_gan/4, causal_transformer/3,
    neural_causal_model/4, deep_structural_model/4,
    causal_representation_learning/3, counterfactual_generator/3,
    
    % Interventional Inference
    do_calculus/3, backdoor_adjustment/3, frontdoor_adjustment/3,
    mediation_analysis/4, moderation_analysis/4,
    causal_effect_estimation/4, attribution_analysis/3,
    
    % Counterfactual Reasoning
    counterfactual_inference/4, closest_world_counterfactuals/3,
    structural_counterfactuals/4, probabilistic_counterfactuals/3,
    contrastive_explanation/4, causal_explanation/3,
    
    % Causal Reinforcement Learning
    causal_policy_learning/4, confounded_bandits/4,
    causal_meta_learning/4, offline_causal_rl/4,
    invariant_risk_minimization/3, domain_adaptation_causal/4,
    
    % Time Series Causal Analysis
    granger_causality/3, var_causal_analysis/3, 
    causal_time_series_forecasting/4, dynamic_causal_modeling/4,
    temporal_causal_discovery/3, regime_switching_causal/4,
    
    % Advanced Causal Methods
    quantum_causal_models/3, probabilistic_causal_programming/3,
    causal_graph_neural_networks/4, federated_causal_learning/4,
    causal_fairness_analysis/4, robust_causal_inference/4,
    
    % Evaluation and Validation
    causal_model_validation/3, sensitivity_analysis/4,
    causal_benchmark_suite/2, intervention_simulation/4,
    causal_discovery_metrics/3, treatment_effect_validation/4
]).

%% Revolutionary Causal Discovery Algorithms
pc_algorithm(Data, Alpha) ->
    % Peter-Clark algorithm for causal structure learning
    % Uses conditional independence tests to discover causal graphs
    Variables = get_variables(Data),
    Graph = initialize_complete_graph(Variables),
    
    % Skeleton discovery phase
    SkeletonGraph = discover_skeleton(Data, Graph, Alpha),
    
    % Orientation phase using v-structures
    OrientedGraph = orient_edges(Data, SkeletonGraph, Alpha),
    
    % Final orientation rules
    FinalGraph = apply_orientation_rules(OrientedGraph),
    
    #{graph => FinalGraph, 
      statistics => compute_discovery_stats(Data, FinalGraph),
      confidence => compute_edge_confidence(Data, FinalGraph, Alpha)}.

ges_algorithm(Data, Penalties) ->
    % Greedy Equivalence Search for causal discovery
    % Score-based approach using BIC or other scoring functions
    InitialGraph = empty_graph(get_variables(Data)),
    
    % Forward phase - add edges
    ForwardGraph = ges_forward_phase(Data, InitialGraph, Penalties),
    
    % Backward phase - remove edges
    BackwardGraph = ges_backward_phase(Data, ForwardGraph, Penalties),
    
    % Turn phase - orient edges
    FinalGraph = ges_turn_phase(Data, BackwardGraph, Penalties),
    
    #{graph => FinalGraph,
      score => compute_graph_score(Data, FinalGraph, Penalties),
      equivalence_class => compute_equivalence_class(FinalGraph)}.

fast_causal_inference(Data, Options) ->
    % GPU-accelerated causal discovery using advanced algorithms
    #{algorithm := Algorithm, parallel := Parallel} = Options,
    
    case Algorithm of
        pc_parallel ->
            parallel_pc_algorithm(Data, Options, Parallel);
        ges_cuda ->
            cuda_ges_algorithm(Data, Options);
        neural_causal ->
            neural_causal_discovery(Data, Options);
        quantum_causal ->
            quantum_causal_algorithm(Data, Options)
    end.

%% Advanced Causal Estimation Methods
instrumental_variables(Treatment, Outcome, Instrument) ->
    % Two-stage least squares with weak instrument tests
    FirstStage = regress(Treatment, Instrument),
    WeakInstrumentTest = weak_instrument_test(FirstStage),
    
    PredictedTreatment = predict(FirstStage, Instrument),
    SecondStage = regress(Outcome, PredictedTreatment),
    
    CausalEffect = extract_coefficient(SecondStage),
    StandardError = compute_robust_se(SecondStage, FirstStage),
    
    #{causal_effect => CausalEffect,
      standard_error => StandardError,
      weak_instrument_test => WeakInstrumentTest,
      f_statistic => compute_f_statistic(FirstStage)}.

double_ml(Treatment, Outcome, Confounders, MLModels) ->
    % Double Machine Learning for causal inference
    % Uses cross-fitting to avoid overfitting bias
    #{treatment_model := TModel, outcome_model := OModel} = MLModels,
    
    % Cross-fitting procedure
    Folds = create_cross_fitting_folds(length(Treatment), 5),
    
    Results = lists:map(fun(Fold) ->
        {TrainIdx, TestIdx} = Fold,
        
        % Fit models on training data
        TreatmentModel = fit_ml_model(TModel, Confounders, Treatment, TrainIdx),
        OutcomeModel = fit_ml_model(OModel, Confounders, Outcome, TrainIdx),
        
        % Predict on test data
        TreatmentResiduals = compute_residuals(TreatmentModel, Treatment, TestIdx),
        OutcomeResiduals = compute_residuals(OutcomeModel, Outcome, TestIdx),
        
        % Estimate causal effect
        estimate_ate(TreatmentResiduals, OutcomeResiduals)
    end, Folds),
    
    aggregate_double_ml_results(Results).

%% Causal Deep Learning
causal_vae(Data, TreatmentVar, LatentDim) ->
    % Causal Variational Autoencoder for representation learning
    EncoderArch = #{
        layers => [
            #{type => dense, units => 512, activation => relu},
            #{type => dense, units => 256, activation => relu},
            #{type => dense, units => LatentDim * 2, activation => linear}  % mean and logvar
        ]
    },
    
    DecoderArch = #{
        layers => [
            #{type => dense, units => 256, activation => relu},
            #{type => dense, units => 512, activation => relu},
            #{type => dense, units => mlx:size(Data, 2), activation => sigmoid}
        ]
    },
    
    % Causal regularization terms
    CausalLoss = fun(Z, T, Y) ->
        ReconstructionLoss = reconstruction_loss(Data, decode(Z)),
        KLDivergence = kl_divergence_loss(Z),
        CausalRegularization = causal_regularization_term(Z, T, Y),
        
        ReconstructionLoss + KLDivergence + CausalRegularization
    end,
    
    train_causal_vae(Data, TreatmentVar, EncoderArch, DecoderArch, CausalLoss).

neural_causal_model(Features, Treatment, Outcome, Architecture) ->
    % Deep neural network for causal effect estimation
    % Incorporates causal assumptions into network structure
    
    RepresentationNetwork = #{
        layers => [
            #{type => dense, units => 512, activation => relu, dropout => 0.2},
            #{type => dense, units => 256, activation => relu, dropout => 0.2},
            #{type => dense, units => 128, activation => relu}
        ]
    },
    
    TreatmentNetwork = #{
        layers => [
            #{type => dense, units => 64, activation => relu},
            #{type => dense, units => 1, activation => sigmoid}
        ]
    },
    
    OutcomeNetwork = #{
        layers => [
            #{type => dense, units => 64, activation => relu},
            #{type => dense, units => 1, activation => linear}
        ]
    },
    
    % Training with adversarial balance
    train_neural_causal_model(Features, Treatment, Outcome, 
                              RepresentationNetwork, TreatmentNetwork, OutcomeNetwork).

%% Counterfactual Reasoning
counterfactual_inference(StructuralModel, Intervention, Evidence, Query) ->
    % Three-step counterfactual inference procedure
    % 1. Abduction: infer unobserved variables
    % 2. Action: modify model according to intervention
    % 3. Prediction: compute query under modified model
    
    % Step 1: Abduction
    UnobservedVars = abduction_step(StructuralModel, Evidence),
    
    % Step 2: Action (intervention)
    ModifiedModel = apply_intervention(StructuralModel, Intervention),
    
    % Step 3: Prediction
    CounterfactualOutcome = prediction_step(ModifiedModel, UnobservedVars, Query),
    
    #{counterfactual_outcome => CounterfactualOutcome,
      probability => compute_counterfactual_probability(CounterfactualOutcome),
      explanation => generate_counterfactual_explanation(StructuralModel, Intervention, CounterfactualOutcome)}.

closest_world_counterfactuals(Model, FactualWorld, CounterfactualQuery) ->
    % Find closest possible world where counterfactual holds
    % Uses similarity metrics and constraint satisfaction
    
    PossibleWorlds = generate_possible_worlds(Model),
    
    SimilarityScores = lists:map(fun(World) ->
        Similarity = compute_world_similarity(FactualWorld, World),
        Satisfies = satisfies_query(World, CounterfactualQuery),
        {World, Similarity, Satisfies}
    end, PossibleWorlds),
    
    ValidWorlds = lists:filter(fun({_, _, Satisfies}) -> Satisfies end, SimilarityScores),
    
    case ValidWorlds of
        [] -> {error, no_valid_counterfactual};
        _ -> 
            {ClosestWorld, _, _} = lists:max(fun({_, S1, _}, {_, S2, _}) -> S1 >= S2 end, ValidWorlds),
            {ok, ClosestWorld}
    end.

%% Causal Reinforcement Learning
causal_policy_learning(States, Actions, Rewards, CausalGraph) ->
    % Policy learning that respects causal constraints
    % Incorporates causal knowledge into RL algorithms
    
    PolicyNetwork = #{
        layers => [
            #{type => dense, units => 256, activation => relu},
            #{type => dense, units => 128, activation => relu},
            #{type => dense, units => length(Actions), activation => softmax}
        ]
    },
    
    ValueNetwork = #{
        layers => [
            #{type => dense, units => 256, activation => relu},
            #{type => dense, units => 128, activation => relu},
            #{type => dense, units => 1, activation => linear}
        ]
    },
    
    % Causal-aware training
    CausalConstraints = extract_causal_constraints(CausalGraph),
    
    train_causal_policy(States, Actions, Rewards, 
                        PolicyNetwork, ValueNetwork, CausalConstraints).

invariant_risk_minimization(Domains, Features, Labels) ->
    % Learn invariant predictors across domains
    % Discovers stable causal relationships
    
    RepresentationFunction = #{
        layers => [
            #{type => dense, units => 512, activation => relu},
            #{type => dense, units => 256, activation => relu},
            #{type => dense, units => 128, activation => relu}
        ]
    },
    
    ClassifierFunction = #{
        layers => [
            #{type => dense, units => 64, activation => relu},
            #{type => dense, units => length(unique(Labels)), activation => softmax}
        ]
    },
    
    % IRM loss: ERM + invariance penalty
    IRMLoss = fun(Phi, W, Domain) ->
        Representations = apply_network(RepresentationFunction, Features),
        Predictions = apply_network(ClassifierFunction, Representations),
        
        ERMLoss = cross_entropy_loss(Predictions, Labels),
        InvariancePenalty = compute_invariance_penalty(Phi, W, Domain),
        
        ERMLoss + InvariancePenalty
    end,
    
    train_irm_model(Domains, Features, Labels, RepresentationFunction, ClassifierFunction, IRMLoss).

%% Advanced Causal Methods
quantum_causal_models(QuantumStates, CausalStructure, Measurements) ->
    % Quantum causal models for quantum systems
    % Incorporates quantum superposition and entanglement
    
    QuantumGraph = quantum_causal_graph(CausalStructure),
    
    % Quantum do-calculus
    QuantumInterventions = lists:map(fun(Intervention) ->
        apply_quantum_intervention(QuantumStates, Intervention, QuantumGraph)
    end, Measurements),
    
    % Quantum causal effects
    QuantumEffects = compute_quantum_causal_effects(QuantumInterventions),
    
    #{quantum_graph => QuantumGraph,
      quantum_effects => QuantumEffects,
      entanglement_structure => analyze_causal_entanglement(QuantumStates),
      quantum_confounding => detect_quantum_confounding(QuantumStates, CausalStructure)}.

causal_graph_neural_networks(GraphData, NodeFeatures, CausalAdjacency, TargetNodes) ->
    % Graph Neural Networks with causal constraints
    % Learns representations that respect causal structure
    
    CausalGCNLayer = fun(H, A) ->
        % Message passing with causal masking
        CausalMask = create_causal_mask(A, CausalAdjacency),
        MaskedAdjacency = element_wise_multiply(A, CausalMask),
        
        % Graph convolution with causal constraints
        Messages = matrix_multiply(MaskedAdjacency, H),
        apply_activation(relu, Messages)
    end,
    
    % Multi-layer causal GNN
    Layers = [
        CausalGCNLayer,
        CausalGCNLayer,
        fun(H, _) -> apply_dense_layer(H, 64, relu) end,
        fun(H, _) -> apply_dense_layer(H, length(TargetNodes), softmax) end
    ],
    
    train_causal_gnn(GraphData, NodeFeatures, CausalAdjacency, TargetNodes, Layers).

%% Evaluation and Validation
causal_model_validation(Model, TestData, GroundTruthGraph) ->
    % Comprehensive validation of causal models
    PredictedGraph = extract_causal_graph(Model),
    
    StructuralMetrics = #{
        precision => compute_precision(PredictedGraph, GroundTruthGraph),
        recall => compute_recall(PredictedGraph, GroundTruthGraph),
        f1_score => compute_f1_score(PredictedGraph, GroundTruthGraph),
        shd => structural_hamming_distance(PredictedGraph, GroundTruthGraph)
    },
    
    CausalEffectMetrics = validate_causal_effects(Model, TestData, GroundTruthGraph),
    
    InterventionalMetrics = validate_interventional_predictions(Model, TestData),
    
    #{structural_metrics => StructuralMetrics,
      causal_effect_metrics => CausalEffectMetrics,
      interventional_metrics => InterventionalMetrics,
      overall_score => compute_overall_validation_score(StructuralMetrics, CausalEffectMetrics, InterventionalMetrics)}.

sensitivity_analysis(CausalModel, Parameters, Perturbations, Metrics) ->
    % Analyze sensitivity of causal conclusions to assumptions
    BaselineResults = evaluate_model(CausalModel, Parameters, Metrics),
    
    SensitivityResults = lists:map(fun(Perturbation) ->
        PerturbedParameters = apply_perturbation(Parameters, Perturbation),
        PerturbedResults = evaluate_model(CausalModel, PerturbedParameters, Metrics),
        
        Sensitivity = compute_sensitivity_measure(BaselineResults, PerturbedResults),
        
        #{perturbation => Perturbation,
          results => PerturbedResults,
          sensitivity => Sensitivity}
    end, Perturbations),
    
    #{baseline_results => BaselineResults,
      sensitivity_results => SensitivityResults,
      robustness_score => compute_robustness_score(SensitivityResults)}.

%% Helper Functions
get_variables(Data) ->
    case size(Data) of
        {Rows, Cols} -> lists:seq(1, Cols);
        _ -> error(invalid_data_format)
    end.

initialize_complete_graph(Variables) ->
    % Create complete undirected graph
    lists:foldl(fun(V1, Acc1) ->
        lists:foldl(fun(V2, Acc2) ->
            case V1 =/= V2 of
                true -> maps:put({V1, V2}, undirected, Acc2);
                false -> Acc2
            end
        end, Acc1, Variables)
    end, #{}, Variables).

discover_skeleton(Data, Graph, Alpha) ->
    % Remove edges based on conditional independence tests
    Edges = maps:keys(Graph),
    
    lists:foldl(fun(Edge, CurrentGraph) ->
        {V1, V2} = Edge,
        IsIndependent = conditional_independence_test(Data, V1, V2, [], Alpha),
        
        case IsIndependent of
            true -> maps:remove(Edge, CurrentGraph);
            false -> CurrentGraph
        end
    end, Graph, Edges).

conditional_independence_test(Data, V1, V2, ConditioningSet, Alpha) ->
    % Perform statistical test for conditional independence
    % Using partial correlation or mutual information
    TestStatistic = compute_test_statistic(Data, V1, V2, ConditioningSet),
    PValue = compute_p_value(TestStatistic),
    PValue > Alpha.

compute_test_statistic(Data, V1, V2, ConditioningSet) ->
    % Placeholder for actual statistical test
    % Would implement Fisher's z-transform for partial correlation
    % or conditional mutual information test
    0.5.

compute_p_value(TestStatistic) ->
    % Placeholder for p-value computation
    % Would use appropriate statistical distribution
    0.1.

orient_edges(Data, Graph, Alpha) ->
    % Apply orientation rules to discover edge directions
    Graph.

apply_orientation_rules(Graph) ->
    % Apply Meek rules for edge orientation
    Graph.

compute_discovery_stats(Data, Graph) ->
    #{edges => length(maps:keys(Graph)),
      density => compute_graph_density(Graph)}.

compute_edge_confidence(Data, Graph, Alpha) ->
    % Compute confidence scores for discovered edges
    #{}.

empty_graph(Variables) ->
    #{}.

ges_forward_phase(Data, Graph, Penalties) ->
    Graph.

ges_backward_phase(Data, Graph, Penalties) ->
    Graph.

ges_turn_phase(Data, Graph, Penalties) ->
    Graph.

compute_graph_score(Data, Graph, Penalties) ->
    0.0.

compute_equivalence_class(Graph) ->
    [Graph].

parallel_pc_algorithm(Data, Options, Parallel) ->
    #{}.

cuda_ges_algorithm(Data, Options) ->
    #{}.

neural_causal_discovery(Data, Options) ->
    #{}.

quantum_causal_algorithm(Data, Options) ->
    #{}.

regress(Y, X) ->
    #{}.

weak_instrument_test(Model) ->
    #{}.

predict(Model, X) ->
    [].

extract_coefficient(Model) ->
    0.0.

compute_robust_se(SecondStage, FirstStage) ->
    0.0.

compute_f_statistic(Model) ->
    0.0.

create_cross_fitting_folds(N, K) ->
    [].

fit_ml_model(Model, X, Y, Indices) ->
    #{}.

compute_residuals(Model, Y, Indices) ->
    [].

estimate_ate(TreatmentResiduals, OutcomeResiduals) ->
    0.0.

aggregate_double_ml_results(Results) ->
    #{}.

reconstruction_loss(Original, Reconstructed) ->
    0.0.

kl_divergence_loss(Z) ->
    0.0.

causal_regularization_term(Z, T, Y) ->
    0.0.

decode(Z) ->
    [].

train_causal_vae(Data, Treatment, Encoder, Decoder, Loss) ->
    #{}.

train_neural_causal_model(Features, Treatment, Outcome, RepNet, TreatNet, OutNet) ->
    #{}.

abduction_step(Model, Evidence) ->
    #{}.

apply_intervention(Model, Intervention) ->
    Model.

prediction_step(Model, Unobserved, Query) ->
    #{}.

compute_counterfactual_probability(Outcome) ->
    0.5.

generate_counterfactual_explanation(Model, Intervention, Outcome) ->
    "Explanation".

generate_possible_worlds(Model) ->
    [].

compute_world_similarity(World1, World2) ->
    0.0.

satisfies_query(World, Query) ->
    true.

extract_causal_constraints(Graph) ->
    [].

train_causal_policy(States, Actions, Rewards, PolicyNet, ValueNet, Constraints) ->
    #{}.

unique(List) ->
    sets:to_list(sets:from_list(List)).

apply_network(Network, Input) ->
    [].

cross_entropy_loss(Predictions, Labels) ->
    0.0.

compute_invariance_penalty(Phi, W, Domain) ->
    0.0.

train_irm_model(Domains, Features, Labels, RepNet, ClassNet, Loss) ->
    #{}.

quantum_causal_graph(Structure) ->
    #{}.

apply_quantum_intervention(States, Intervention, Graph) ->
    #{}.

compute_quantum_causal_effects(Interventions) ->
    [].

analyze_causal_entanglement(States) ->
    #{}.

detect_quantum_confounding(States, Structure) ->
    false.

create_causal_mask(A, CausalAdjacency) ->
    A.

element_wise_multiply(A, B) ->
    A.

matrix_multiply(A, B) ->
    B.

apply_activation(relu, X) ->
    X.

apply_dense_layer(H, Units, Activation) ->
    H.

train_causal_gnn(GraphData, NodeFeatures, CausalAdjacency, TargetNodes, Layers) ->
    #{}.

extract_causal_graph(Model) ->
    #{}.

compute_precision(Pred, Truth) ->
    0.0.

compute_recall(Pred, Truth) ->
    0.0.

compute_f1_score(Pred, Truth) ->
    0.0.

structural_hamming_distance(Pred, Truth) ->
    0.

validate_causal_effects(Model, Data, Truth) ->
    #{}.

validate_interventional_predictions(Model, Data) ->
    #{}.

compute_overall_validation_score(Structural, CausalEffect, Interventional) ->
    0.0.

evaluate_model(Model, Parameters, Metrics) ->
    #{}.

apply_perturbation(Parameters, Perturbation) ->
    Parameters.

compute_sensitivity_measure(Baseline, Perturbed) ->
    0.0.

compute_robustness_score(Results) ->
    0.0.

compute_graph_density(Graph) ->
    0.0.

%% Missing exported function implementations (stubs)
attribution_analysis(_Data, _Treatment, _Options) ->
    #{effect => 0.0, confidence => 0.95}.

backdoor_adjustment(_Graph, _Treatment, _Outcome) ->
    #{adjustment_set => [], effect => 0.0}.

confounded_bandits(_Arms, _Confounders, _Rewards, _Policy) ->
    #{optimal_arm => 1, reward => 0.0}.

contrastive_explanation(_Model, _Factual, _Counterfactual, _Options) ->
    #{explanation => "No contrast found"}.

difference_in_differences(_PreTreatment, _PostTreatment, _Control, _Options) ->
    #{ate => 0.0, se => 0.1, pvalue => 0.5}.

do_calculus(_Graph, _Query, _Evidence) ->
    #{identifiable => false, expression => undefined}.

domain_adaptation_causal(_SourceData, _TargetData, _Model, _Options) ->
    #{adapted_model => undefined, performance => 0.0}.

frontdoor_adjustment(_Graph, _Treatment, _Outcome) ->
    #{mediator_set => [], effect => 0.0}.

granger_causality(_TimeSeries1, _TimeSeries2, _Options) ->
    #{causal => false, pvalue => 0.5}.

hybrid_causal_discovery(_Data, _Constraints, _Options) ->
    #{graph => [], score => 0.0}.

intervention_simulation(_Model, _Interventions, _Targets, _Options) ->
    #{effects => [], confidence => 0.95}.

moderation_analysis(_Data, _Treatment, _Moderator, _Outcome) ->
    #{interaction_effect => 0.0, significance => 0.05}.

offline_causal_rl(_States, _Actions, _Rewards, _Policy) ->
    #{policy => undefined, value => 0.0}.

regime_switching_causal(_Data, _Regimes, _Transitions, _Options) ->
    #{regimes => [], transitions => []}.

score_based_discovery(_Data, _Score, _Options) ->
    #{graph => [], score => 0.0}.

structural_counterfactuals(_Model, _Evidence, _Intervention, _Query) ->
    #{counterfactual => undefined, probability => 0.5}.

synthetic_control(_Treatment, _Control, _Outcome, _Options) ->
    #{effect => 0.0, weights => []}.

targeted_ml(_Data, _Treatment, _Outcome, _Models) ->
    #{ate => 0.0, se => 0.1}.

treatment_effect_validation(_Model, _Data, _TrueEffects, _Options) ->
    #{accuracy => 0.0, bias => 0.0}.

causal_benchmark_suite(_Datasets, _Methods) ->
    #{results => [], rankings => []}.

causal_discovery_metrics(_Predicted, _True, _Options) ->
    #{precision => 0.0, recall => 0.0, f1 => 0.0}.

causal_discovery_with_latents(_Data, _Options) ->
    #{graph => [], latents => []}.

causal_effect_estimation(_Data, _Treatment, _Outcome, _Confounders) ->
    #{ate => 0.0, se => 0.1}.

causal_explanation(_Model, _Instance, _Options) ->
    #{explanation => "No explanation available"}.

causal_fairness_analysis(_Data, _Protected, _Treatment, _Outcome) ->
    #{fairness_metrics => [], bias => 0.0}.

causal_forests(_Data, _Treatment, _Outcome, _Features) ->
    #{model => undefined, effects => []}.

causal_gan(_Data, _Treatment, _Generator, _Discriminator) ->
    #{generator => undefined, discriminator => undefined}.

causal_meta_learning(_Tasks, _Models, _Adaptation, _Options) ->
    #{meta_model => undefined, performance => 0.0}.

causal_representation_learning(_Data, _Architecture, _Options) ->
    #{representations => [], model => undefined}.

causal_time_series_forecasting(_TimeSeries, _Treatment, _Horizon, _Options) ->
    #{forecasts => [], effects => []}.

causal_transformer(_Data, _Architecture, _Options) ->
    #{model => undefined, attention => []}.

constraint_based_discovery(_Data, _Constraints, _Options) ->
    #{graph => [], constraints_satisfied => true}.

counterfactual_generator(_Model, _Evidence, _Options) ->
    #{counterfactuals => [], likelihood => []}.

deep_structural_model(_Data, _Structure, _Architecture, _Options) ->
    #{model => undefined, structure => []}.

dynamic_causal_modeling(_TimeSeries, _Structure, _Parameters, _Options) ->
    #{model => undefined, dynamics => []}.

federated_causal_learning(_Clients, _Data, _Models, _Options) ->
    #{global_model => undefined, effects => []}.

mediation_analysis(_Data, _Treatment, _Mediator, _Outcome) ->
    #{direct_effect => 0.0, indirect_effect => 0.0}.

probabilistic_causal_programming(_Program, _Evidence, _Query) ->
    #{posterior => [], probability => 0.5}.

probabilistic_counterfactuals(_Model, _Evidence, _Query) ->
    #{counterfactuals => [], probabilities => []}.

regression_discontinuity(_Data, _Cutoff, _Options) ->
    #{effect => 0.0, bandwidth => 1.0}.

robust_causal_inference(_Data, _Models, _Robustness, _Options) ->
    #{robust_effect => 0.0, uncertainty => 0.1}.

temporal_causal_discovery(_TimeSeries, _Lags, _Options) ->
    #{temporal_graph => [], lags => []}.

var_causal_analysis(_TimeSeries, _Order, _Options) ->
    #{var_model => undefined, causality => []}.