fixing typos

Signed-off-by: Nathaniel <[email protected]>

Author: NathanielF

docs/source/knowledgebase/structural_causal_models.ipynb

@@ -3730,7 +3730,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The `bart_outcome` model places weight on the correlation between treatment and outcome rather than parcel out the share of impact into the treatment and confounding relationship. The causal effect absorbed into the covariate adjustment of the BART component, and we have a fundamental misattribution which makes recovery of structural parameter impossible in this set up. The other two BART model specifications; `bart_treatment` and `bart_treatment_cate` correctly identify the structural parameter because the BART component is used to flexibily model the treatment status. The structural parameter $\\alpha$ remains identifiable as the average or baseline effect because we've partialied out the variation in the outcome explicitly. The more traditional `linear_no_bart` model does not have the flexibility to absorb the causal effect into a non-linear component. As such, the structural parameter remains identifiable. This is one of the virtues of \"simpler\" models. \n",
+    "The `bart_outcome` model places weight on the correlation between treatment and outcome rather than parcel out the share of impact into the treatment and confounding relationship. The causal effect absorbed into the covariate adjustment of the BART component, and we have a fundamental misattribution which makes recovery of structural parameter impossible in this set up. The other two BART model specifications; `bart_treatment` and `bart_treatment_cate` correctly identify the structural parameter because the BART component is used to flexibly model the treatment status. The structural parameter $\\alpha$ remains identifiable as the average or baseline effect because we've partialied out the variation in the outcome explicitly. The more traditional `linear_no_bart` model does not have the flexibility to absorb the causal effect into a non-linear component. As such, the structural parameter remains identifiable. This is one of the virtues of \"simpler\" models. \n",
     "\n",
     "### Non-Parametric Causal Inference\n",
     "\n",
@@ -4095,7 +4095,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The results are striking in their consistency. For the three successful specifications, both methods of extracting causal effects agree. For the `bart_outcome` specfication the Imputation approach to causal inference also fails. This is crucial. The failure is not about how we interrogate the model, but about what the model learned during fitting."
+    "The results are striking in their consistency. For the three successful specifications, both methods of extracting causal effects agree. For the `bart_outcome` specification the Imputation approach to causal inference also fails. This is crucial. The failure is not about how we interrogate the model, but about what the model learned during fitting."
    ]
   },
   {
@@ -4174,7 +4174,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "In prediction tasks, BART's flexibility is a pure advantage. It finds patterns we didn't know to look for, captures complex interactions automatically, and often achieves superior out-of-sample accuracy. But in causal inference, this same flexibility becomes a liability when it absorbs the variation we're trying to causally attribute. The problem is **structural**: any sufficiently flexible method faces this challenge. Methods that can perfectly adapt their functional form to training data will inadvertently learn causal pathways as associational patterns, unless the structure learning is constrainted to partial out the treatment influences. The stronger the relationship between the predictors of the outcome and the treatment, the more we can expect to see this collapse. Flexible outcome modelling may be useful in cases where the relationship between treatment and covariates is truly independent, but it presents a risk where the focus is on recovering treatment effects."
+    "In prediction tasks, BART's flexibility is a pure advantage. It finds patterns we didn't know to look for, captures complex interactions automatically, and often achieves superior out-of-sample accuracy. But in causal inference, this same flexibility becomes a liability when it absorbs the variation we're trying to causally attribute. The problem is **structural**: any sufficiently flexible method faces this challenge. Methods that can perfectly adapt their functional form to training data will inadvertently learn causal pathways as associational patterns, unless the structure learning is constrained to partial out the treatment influences. The stronger the relationship between the predictors of the outcome and the treatment, the more we can expect to see this collapse. Flexible outcome modelling may be useful in cases where the relationship between treatment and covariates is truly independent, but it presents a risk where the focus is on recovering treatment effects."
    ]
   },
   {